Sequence-based signal processing method and apparatus

ABSTRACT

A sequence-based signal processing method and apparatus are provided. A sequence meeting a requirement for sending a signal by using a physical uplink control channel (PUCCH) is determined, where the sequence is a sequence {f n } consisting of N elements, f n  is an element in the sequence {f n }, and the determined sequence {f n } is a sequence meeting a preset condition; then, the N elements in the sequence {f n } are respectively mapped to N subcarriers to generate a first signal; and the first signal is sent. By using the determined sequence, when a signal is sent by using a PUCCH, a low sequence correlation can be maintained, and a relatively small peak-to-average power ratio (PAPR) value and cubic metric (CM) value can also be maintained, thereby meeting a requirement of a communication application environment in which a signal is sent by using a PUCCH.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of International Application No.PCT/CN2018/096168, filed on Jul. 18, 2018, which claims priority toChinese Patent Application No. 201710806190.X, filed on Sep. 8, 2017 andChinese Patent Application No. 201711140559.4, filed on Nov. 16, 2017.All of the aforementioned patent applications are hereby incorporated byreference in their entireties.

TECHNICAL FIELD

Embodiments of this application relate to the field of communicationstechnologies, and in particular, to a sequence-based signal processingmethod and apparatus.

BACKGROUND

In a Long Term Evolution (LTE) system, a physical uplink control channel(PUCCH) occupies, for sending uplink control information (UCI), 13 or 14orthogonal frequency division multiplexing (OFDM) symbols or discreteFourier transform spread orthogonal frequency division multiplexing(DFT-s-OFDM) symbols in one subframe. A PUCCH format 1a/1b is used totransmit response information of 1 or 2 bits, and the PUCCH format 1a/1bis sent in a sequence modulation manner. Generally, in the LTE system,to avoid interference between PUCCHs in two neighboring cells, sequencesselected for the neighboring cells need to have a low correlation witheach other. To expand coverage of a PUCCH, it is necessary to ensurethat all sent signals have relatively small peak to average power ratio(PAPR) values and cubic metric (CM) values.

Currently, in the LTE system, there are 30 existing length-N rootsequences x_(i), i=0, 1, . . . , N−1, where N=12, 18, 24, or 6. The rootsequence is used for sending UCI or a demodulation reference signal(DMRS) by using a PUCCH format 1a/1b in the LTE system. However, inpreliminary design of the LTE system, optimization of the CM value andthe sequence correlation is mainly considered for the 30 length-N rootsequences. A relationship between the CM value and the PAPR value is:the PAPR may not be small if the CM value is small. Therefore, it cannotbe ensured that PAPR values are small when it is ensured that all the 30length-N root sequences have relatively small CM values and lowcorrelations.

A length-24 CGS in LTE has a relatively large PAPR, and PAPR values areas follows:

3.4088, 3.7273, 3.5504, 3.5747, 3.6863, 3.5919, 3.9650, 3.8684, 4.2962,3.2399, 4.1349, 2.9308, 3.3087, 4.0994, 3.7059, 3.7320, 4.0424, 4.0889,3.0390, 3.4151, 3.9811, 4.2336, 4.1542, 3.5316, 2.8697, 2.6239, 3.2999,3.8447, 3.8657, and 3.7505.

PAPRs of length-18 sequences in LTE are as follows: 3.3052, 3.0602,3.2669, 3.7847, 3.5747, 3.6053, 3.3331, 3.1714, 3.1280, 3.7510, 2.9786,3.4392, 3.0917, 3.6472, 3.4528, 3.4566, 3.8168, 3.1846, 3.0146, 3.4002,3.1365, 3.7687, 3.1833, 3.9640, 3.9144, 3.4006, 3.4189, 3.6522, 2.8956,and 3.8309.

PAPRs of length-6 sequences in LTE are as follows: 3.5139, 3.5139,4.1492, 3.0076, 4.0755, 4.2597, 4.1492, 4.1492, 2.9721, 3.1240, 4.2597,4.2597, 4.0755, 3.0076, 4.0755, 2.8129, 2.9721, 4.1492, 3.0076, 3.0076,4.1492, 2.8129, 3.0076, 3.5139, 3.5139, 4.0755, 4.1492, 4.1492, 4.0755,and 4.2597. It can be seen that not a few PAPR values are greater than 3dB.

SUMMARY

In view of this, embodiments of this application provide asequence-based signal processing method, a signal processing apparatus,and a communications system, to resolve a prior-art problem that 30existing root sequences cannot meet a requirement of an existingcommunication application environment in which a signal is sent by usinga PUCCH.

A first aspect of the embodiments of this application provides asequence-based signal processing method, including: determining asequence {f_(n)} consisting of N elements, where f_(n) is an element inthe sequence {f_(n)}, the sequence {f_(n)} is a sequence meeting apreset condition, the preset condition is f_(n)=A·x_(n)·e^(2π·j·a·n), avalue of n ranges from 0 to N−1, A is a non-zero complex number, a is areal number, j=√{square root over (−1)}, an element x_(n)=u·e^(π·j·s)^(n) ^(/4), u is a non-zero complex number, a sequence {s_(n)}consisting of elements s_(n) is a sequence in a first sequence set or anequivalent sequence of a sequence in the first sequence set, or asequence in a second sequence set or an equivalent sequence of asequence in the second sequence set, or a sequence in a third sequenceset or an equivalent sequence of a sequence in the third sequence set,and for the sequences in the first sequence set, the second sequenceset, and the third sequence set herein, refer to descriptions in thespecification; mapping the sequence {f_(n)} to N subcarriers to generatea first signal; and sending the first signal.

In the foregoing solution, by using the determined sequence, when asignal is sent by using a PUCCH, a low sequence correlation can bemaintained, and a relatively small PAPR value and CM value can also bemaintained, thereby meeting a requirement of a communication applicationenvironment in which a signal is sent by using a PUCCH.

In a possible design, the mapping the sequence {f_(n)} to N subcarriersincludes: respectively mapping the N elements in the sequence {f_(n)} toN consecutive subcarriers; or respectively mapping the N elements in thesequence {f_(n)} to N equally spaced subcarriers.

In a possible design, the first signal is a reference signal, or thefirst signal is a signal used to carry communication information.

In a possible design, the sequence {s_(n)} consisting of the elementss_(n) is a sequence in a fourth sequence set or an equivalent sequenceof a sequence in the fourth sequence set. For the sequence in the fourthsequence set herein, refer to descriptions in the specification.

In a possible design, a set including the sequence {s_(n)} consisting ofthe elements s_(n) includes some or all of sequences in a fifth sequenceset or some or all of equivalent sequences of sequences in the fifthsequence set. For the sequence in the fifth sequence set herein, referto descriptions in the specification.

In a possible design, the sequence {s_(n)} consisting of the elementss_(n) is a sequence in a sixth sequence set or an equivalent sequence ofa sequence in the sixth sequence set. For the sequence in the sixthsequence set herein, refer to descriptions in the specification.

In a possible design, the equivalent sequence is {q_(n)}, the equivalentsequence {q_(n)} meets q_(n)=s_(n)+u_(n) (mod 8), a sequence {u_(n)}consisting of u_(n) meets u_(n)=f+g·n(mod 8), f∈{0,2,4,6}, andg∈{0,2,4,6}.

A second aspect of the embodiments of this application provides asequence-based signal processing method, and the signal processingmethod includes: receiving a first signal carried on N subcarriers;obtaining N elements in a sequence {f_(n)}, where the first signal isgenerated by mapping the sequence {f_(n)} to the N subcarriers, f_(n) isan element in the sequence {f_(n)}, the sequence {f_(n)} is a sequencemeeting a preset condition, the preset condition isf_(n)=A·x_(n)·e^(2π·j·a·n), a value of n ranges from 0 to N−1, A is anon-zero complex number, a is a real number, an elementx_(n)=u·exp(π·j·s_(n)/4), u is a non-zero complex number, a sequence{s_(n)} consisting of elements s_(n) is a sequence in a first sequenceset or an equivalent sequence of a sequence in the first sequence set,or a sequence in a second sequence set or an equivalent sequence of asequence in the second sequence set, or a sequence in a third sequenceset or an equivalent sequence of a sequence in the third sequence set,and for the sequences in the first sequence set, the second sequenceset, and the third sequence set herein, refer to descriptions in thespecification; and processing the first signal based on the N elementsin the sequence {f_(n)}.

In the foregoing solution, by using the determined sequence, when asignal is sent by using a PUCCH, a low sequence correlation can bemaintained, and a relatively small PAPR value and CM value can also bemaintained, thereby meeting a requirement of a communication applicationenvironment in which a signal is sent by using a PUCCH.

In a possible design, the receiving a first signal carried on Nsubcarriers includes: obtaining the first signal on the N subcarriers onN consecutive subcarriers; or obtaining the first signal on the Nsubcarriers on N equally spaced subcarriers.

In a possible design, the first signal is a reference signal, or thefirst signal is a signal used to carry communication information.

In a possible design, the sequence {s_(n)} consisting of the elementss_(n) is a sequence in a fourth sequence set or an equivalent sequenceof a sequence in the fourth sequence set. For the sequence in the fourthsequence set herein, refer to descriptions in the specification.

In a possible design, a set including the sequence {s_(n)} consisting ofthe elements s_(n) includes some or all of sequences in a fifth sequenceset or some or all of equivalent sequences of sequences in the fifthsequence set. For the sequence in the fifth sequence set herein, referto descriptions in the specification.

In a possible design, the sequence {s_(n)} consisting of the elementss_(n) is a sequence in a sixth sequence set or an equivalent sequence ofa sequence in the sixth sequence set. For the sequence in the sixthsequence set herein, refer to descriptions in the specification.

In a possible design, the equivalent sequence is {q_(n)}, the equivalentsequence {q_(n)} meets q_(n)=s_(n)+u_(n) (mod 8), a sequence {u_(n)}consisting of u_(n) meets u_(n)=f+g·n(mod 8), f∈{0,2,4,6}, andg∈{0,2,4,6}.

A third aspect of the embodiments of this application provides a signalprocessing apparatus, the signal processing apparatus may be acommunications device, or may be a chip in a communications device, andthe communications device or the chip has a function of performing thesequence-based signal processing method according to any one of thefirst aspect and the possible designs of the first aspect. The functionmay be implemented by hardware, or may be implemented by hardware byexecuting corresponding software. The hardware or the software includesone or more units corresponding to the function.

The communications device includes a processing unit and a transceiverunit. The processing unit may be a processor, the transceiver unit maybe a transceiver, and the transceiver includes a radio frequencycircuit. Optionally, the communications device further includes astorage unit, and the storage unit may be, for example, a memory. Whenthe communications device includes the storage unit, the storage unit isconfigured to store a computer executable instruction, the processingunit is connected to the storage unit, and the processing unit executesthe computer executable instruction stored in the storage unit, so thatthe communications device performs the sequence-based signal processingmethod according to any one of the first aspect and the possible designsof the first aspect.

The chip includes a processing unit and a transceiver unit. Theprocessing unit may be a processor, and the transceiver unit may be aninput/output interface, a pin, a circuit, or the like in the chip. Theprocessing unit may execute a computer executable instruction stored ina storage unit, so that the chip performs the sequence-based signalprocessing method according to any one of the first aspect and thepossible designs of the first aspect. Optionally, the storage unit maybe a storage unit (for example, a register or a buffer) in the chip, orthe storage unit may be a storage unit (for example, a read-only memory(ROM)) or another type of static storage device (for example, a randomaccess memory (RAM)) that may store static information and aninstruction that is in the communications device and that is outside thechip.

The processor mentioned in the third aspect may be a central processingunit (CPU), a microprocessor, or an application-specific integratedcircuit (ASIC), or may be one or more integrated circuits configured tocontrol program execution of the sequence-based signal processing methodaccording to any one of the first aspect and the possible designs of thefirst aspect.

A fourth aspect of the embodiments of this application provides a signalprocessing apparatus, the signal processing apparatus may be acommunications device, or may be a chip in a communications device, andthe communications device or the chip has a function of performing thesequence-based signal processing method according to any one of thesecond aspect and the possible designs of the second aspect. Thefunction may be implemented by hardware, or may be implemented byhardware by executing corresponding software. The hardware or thesoftware includes one or more units corresponding to the function.

The communications device includes a processing unit and a transceiverunit. The processing unit may be a processor, the transceiver unit maybe a transceiver, and the transceiver includes a radio frequencycircuit. Optionally, the communications device further includes astorage unit, and the storage unit may be, for example, a memory. Whenthe communications device includes the storage unit, the storage unit isconfigured to store a computer executable instruction, the processingunit is connected to the storage unit, and the processing unit executesthe computer executable instruction stored in the storage unit, so thatthe communications device performs the sequence-based signal processingmethod according to any one of the second aspect and the possibledesigns of the second aspect.

The chip includes a processing unit and a transceiver unit. Theprocessing unit may be a processor, and the transceiver unit may be aninput/output interface, a pin, a circuit, or the like in the chip. Theprocessing unit may execute a computer executable instruction stored ina storage unit, so that the chip performs the sequence-based signalprocessing method according to any one of the second aspect and thepossible designs of the second aspect. Optionally, the storage unit maybe a storage unit (for example, a register or a buffer) in the chip, orthe storage unit may be a storage unit (for example, a read-only memory(ROM)) or another type of static storage device (for example, a randomaccess memory (RAM)) that may store static information and aninstruction that is in the communications device and that is outside thechip.

The processor mentioned in the fourth aspect may be a central processingunit (CPU), a microprocessor, or an application-specific integratedcircuit (ASIC), or may be one or more integrated circuits configured tocontrol program execution of the sequence-based signal processing methodaccording to any one of the second aspect and the possible designs ofthe second aspect.

A fifth aspect of the embodiments of this application provides acommunications system, and the communications system includes thecommunications device provided in the third aspect of the embodiments ofthis application and the communications device provided in the fourthaspect of the embodiments of this application.

A sixth aspect of the embodiments of this application provides acomputer readable storage medium, configured to store a computerinstruction, and when the computer instruction runs on a computer, thecomputer performs the sequence-based signal processing method accordingto the first aspect or the second aspect of the embodiments of thisapplication.

A seventh aspect of the embodiments of this application provides acomputer program product including an instruction, and when the computerprogram product runs on a computer, the computer performs thesequence-based signal processing method according to the first aspect orthe second aspect of the embodiments of this application.

An eighth aspect of the embodiments of this application provides a chip,and the chip includes an input interface, an output interface, at leastone memory, and at least one processor. The at least one memory isconfigured to store code, the at least one processor is configured toexecute the code in the memory, and when executing the code, theprocessor performs the sequence-based signal processing method accordingto the first aspect or the second aspect of the embodiments of thisapplication.

According to the sequence-based signal processing method, the signalprocessing apparatus, the communications system, the computer readablestorage medium, the computer program product, and the chip disclosed inthe embodiments of this application, a sequence meeting a requirementfor sending a signal by using a PUCCH is determined, where the sequenceis the sequence {f_(n)} consisting the N elements, f_(n) is an elementin the sequence {f_(n)}, and the determined sequence {f_(n)} is asequence meeting the preset condition; then, the N elements in thesequence {f_(n)} are respectively mapped to the N subcarriers togenerate the first signal; and the first signal is sent. By using thedetermined sequence, when a signal is sent by using a PUCCH, a lowsequence correlation can be maintained, and a relatively small PAPRvalue and CM value can also be maintained, thereby meeting a requirementof a communication application environment in which a signal is sent byusing a PUCCH.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic flowchart of a sequence-based signal sendingprocessing method according to an embodiment of this application;

FIG. 2 is a schematic flowchart of determining a sequence {f_(n)} by aterminal according to an embodiment of this application;

FIG. 3 is a schematic flowchart of generating and sending a first signalby a terminal according to an embodiment of this application;

FIG. 4a and FIG. 4b are schematic diagrams of mapping a sequence {f_(n)}consisting of N elements to N subcarriers according to an embodiment ofthis application;

FIG. 5 is a schematic diagram of processing a first signal by a networkdevice according to an embodiment of this application;

FIG. 6 is a schematic structural diagram of a terminal according to anembodiment of this application;

FIG. 7 is a schematic structural diagram of another terminal accordingto an embodiment of this application;

FIG. 8 is a schematic structural diagram of a network device accordingto an embodiment of this application;

FIG. 9 is a schematic structural diagram of another network deviceaccording to an embodiment of this application; and

FIG. 10 is a schematic structural diagram of a communications systemaccording to an embodiment of this application.

DESCRIPTION OF EMBODIMENTS

Embodiments of this application provide a sequence-based signalprocessing method, a related device, and a communications system. Asequence meeting a requirement for sending a signal by using a PUCCH isdetermined, so that when a signal is sent by using a PUCCH, a lowsequence correlation can be maintained, and a relatively small PAPRvalue and CM value can also be maintained, thereby meeting a requirementof a communication application environment in which a signal is sent byusing a PUCCH.

In the embodiments, the claims, and the accompanying drawings of thisapplication, terms “first”, “second”, and the like are intended todistinguish between different objects but do not indicate a particularorder. In addition, the terms “include” and “with” are not exclusive.For example, a process, a method, a system, a product, or a deviceincluding a series of steps or units is not limited to the listed stepsor units, and may further include steps or units that are not listed.

Currently, in an LTE system, a 4G system, a 4.5G system, and a 5Gsystem, sending UCI and a DMRS by using a PUCCH can be supported. Toimprove coverage performance of the PUCCH, the PUCCH is sent in asequence modulation manner. To be specific, on all OFDM symbols fortransmitting UCI, a to-be-sent signal is modulated onto a computergenerated sequence (CGS). CGSs are screened to ensure that all sentsignals have relatively small PAPR values and CM values, therebyexpanding PUCCH coverage. The PUCCH is also used at a cell boundary. Fora user at the cell boundary, a sequence correlation further needs to beconsidered during CGS screening.

For example, a first cell and a second cell are neighboring cells. If afirst sequence used by the first cell is highly correlated with a secondsequence used by the second cell, at a boundary of the first cell, aPUCCH sent by user equipment in the first cell may interfere withreceiving a signal by a base station of the second cell by using aPUCCH. Consequently, PUCCH receiving performance is degraded. Therefore,sequences with a low correlation need to be determined during CGSscreening.

To ensure that, in the LTE system, the 4G system, the 4.5G system, the5G system, and even another communications system or a communicationapplication environment with a higher requirement, when UCI and a DMRSare sent by using a PUCCH, relatively small PAPR values and CM valuescan be maintained, and a low sequence correlation can also bemaintained, the embodiments of this application provide a specificimplementation process of sequence-based signal processing. The processis described in detail in the following embodiments.

In the embodiments of this application, sequence-based signal processingis described mainly from a receiver side and a transmitter side in acommunications system or a communication application environment. Thereceiver side may be a network device, and the transmitter side may be aterminal; or the receiver side may be a terminal, and the transmitterside may be a network side. In the following embodiments, an example inwhich the receiver side is a network device and the transmitter side isa terminal is used for description, but the present invention is notlimited thereto.

The terminal in the embodiments of this application may be userequipment. The user equipment may be a wired device or may be a wirelessdevice. The wireless device may be a handheld device with a wirelessconnection function, another processing device connected to a wirelessmodem, or a mobile terminal that communicates with one or more corenetworks by using a radio access network. For example, the wirelessterminal may be a mobile phone, a computer, a tablet computer, apersonal digital assistant (PDA), a mobile internet device (MID), awearable device, or an e-book reader. For another example, the wirelessterminal may be a portable, pocket-sized, handheld, computer built-in,or in-vehicle mobile device. For another example, the wireless terminalmay be a mobile station or an access point.

The network device in the embodiments of this application may be a basestation. The base station may include various forms of macro basestations, micro base stations, relay nodes, access point base stationcontrollers, transmission and reception points, and the like. In systemsusing different radio access technologies, the base station may havedifferent specific names.

As shown in FIG. 1, FIG. 1 is a schematic flowchart of a sequence-basedsignal processing method according to an embodiment of this application.The method includes the following steps.

S101. A terminal determines a sequence {f_(n)} consisting of N elements.N is a positive integer greater than 1, for example, may be 6, 18, or24.

Optionally, the determining a sequence {f_(n)} consisting of N elementsin S101 may be performed by the terminal after the terminal accesses anetwork. Alternatively, after the terminal accesses a network, a networkdevice determines a sequence {x_(n)} and configures the sequence {x_(n)}for the terminal, and the terminal determines, based on the sequence{x_(n)}, the sequence {f_(n)} consisting the N elements.

During specific implementation, f_(n) is an element in the sequence{f_(n)}, and the determined sequence {f_(n)} is a sequence meeting apreset condition. The preset condition is f_(n)=A·x_(n)·e^(2π·j·a·n).Herein n is an integer, and a value of n ranges from 0 to N−1. A is anon-zero complex number, a is a real number, j=√{square root over (−1)},exp(2π·j·a·n) indicates e^(2π·j·a·n), an elementx_(n)=u·exp(π·j·s_(n)/4), and u is a non-zero complex number.

A sequence {s_(n)} consisting of elements s_(n) is a sequence in a firstsequence set or an equivalent sequence of a sequence in the firstsequence set, or a sequence in a second sequence set or an equivalentsequence of a sequence in the second sequence set, or a sequence in athird sequence set or an equivalent sequence of a sequence in the thirdsequence set.

A length of the sequence in the first sequence set is 18, and thesequence in the first sequence set includes a sequence in a sequence set1A and/or a sequence in a sequence set 1B.

The sequence in the sequence set 1A includes some or all of thefollowing 208 sequences, and PAPRs of {f_(n)} corresponding to thesequences and equivalent sequences of the sequences are all less than2.6 dB:

{3, −1, 1, −3, −3, 1, 3, 1, −3, −3, 1, −1, 3, −3, −3, −3, −3, −3}, {1,−1, 3, 1, 3, 1, −3, −3, 1, 1, 3, 3, −1, 1, −3, −1, −3, −3}, {−1, −1, 3,1, 3, 3, −1, 3, −3, −1, 3, −1, −3, −1, 1, −1, −3, −3}, {−1, −3, −3, −3,1, −3, −1, 1, −3, 1, −3, 3, −1, −1, 3, 3, −3, −3}, {−1, −3, 3, −1, 3,−1, 3, −3, 3, 3, 3, 3, 3, −3, −1, 1, −3, −3}, {−3, 1, 3, −3, 3, −1, 1,3, 1, −1, 3, −3, 3, 1, −3, −3, −3, −3}, {3, 1, −3, 3, 1, −3, 1, 3, 1, 1,3, −3, 1, 1, 1, −3, −3, −3}, {1, −1, 3, −3, 3, 1, −3, −3, 3, −3, −1, 3,−1, −1, −1, 1, −3, −3}, {3, −1, 3, −1, 3, −3, −3, 3, 3, −1, −1, −3, −1,−1, 3, 3, −3, −3}, {1, 1, −1, −1, −3, 1, −3, −3, 1, 3, −1, −3, 1, 3, 3,3, −3, −3}, {3, 3, 1, 1, 1, −1, 3, −1, 1, −3, 1, 1, −3, 3, 1, 3, −3,−3}, {−1, −1, −3, 3, −3, −1, 3, 3, −1, 3, 1, −3, 1, 3, 3, 3, −3, −3},{1, −3, 1, 3, −3, 1, −3, 3, −1, −1, −3, 3, −1, −1, −1, −3, −3, −3}, {1,1, −1, 3, 3, 3, 1, −3, 3, −1, 1, −3, −1, −1, −1, 3, −3, −3}, {1, 3, 1,3, −3, 1, −3, 3, 1, 3, 1, −1, 1, 3, 1, −1, −3, −3}, {3, 1, −3, 3, −1, 3,−3, 3, −3, −1, −1, 1, 3, −1, −1, −3, −3, −3}, {−1, 1, 1, −3, 3, −1, −3,−1, 3, −3, 3, −3, 3, 3, −1, −1, −3, −3}, {1, −3, −3, 3, 1, −3, 1, −3,−1, −3, −1, −1, −3, −1, 3, 3, −3, −3}, {−3, 1, 1, −1, 3, −1, 3, −3, −1,1, 3, 1, −3, −3, −3, 3, −3, −3}, {1, −3, 1, −3, −3, 1, −3, 1, 1, −3, −3,1, 1, −3, −3, −3, −3, −3}, {1, 3, −1, 3, −1, 1, −1, −1, −1, 3, 3, 3, 1,−3, 3, 1, −3, −3}, {3, 3, −1, 1, −1, −1, 3, −1, −3, 3, −1, 3, −3, 3, 1,3, −3, −3}, {3, −3, −1, 3, −1, 3, −1, −3, −1, −1, −1, −1, −1, −3, 3, 1,−3, −3}, {3, −1, −1, −1, −3, 3, −3, −1, 1, −3, −1, 3, 1, −3, 3, 3, −3,−3}, {3, 1, 3, 3, 1, −3, 3, −3, 1, 3, 1, −1, −3, −1, 1, 1, −3, −3}, {−1,3, 1, −3, −3, −1, 3, −3, 3, 1, −1, −1, 3, −3, 3, −3, −3, −3}, {−1, 3,−1, 1, −1, 1, 1, −3, 3, 1, −1, 1, 1, 3, −1, −1, −3, −3}, {−3, 1, 1, −3,3, 3, −3, −1, −3, −1, 3, 1, −3, −1, −1, −3, −3, −3}, {3, 3, −3, 3, 1, 3,3, −3, −1, 3, −1, 1, 3, 3, 1, −1, −3, −3}, {−1, 3, 1, 3, 3, −1, −3, −1,3, 1, 3, −1, −1, −3, −3, −1, −3, −3}, {−1, 3, 3, −3, 1, −3, 1, −3, −3,3, −1, −1, −1, −1, −1, 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−1, 1, 3, 3, −3, −3}, {1, −1, −3, −3, 1, −3, 1, −3, 1, 1,−3, 1, 1, 1, 1, 3, −3, −3}, {1, 3, −1, −1, 3, 3, −1, 3, −1, 1, −1, −3,3, −3, 3, −3, −3, −3}, {−1, 3, −3, −1, 3, 3, 3, −3, 3, −1, −3, −1, −3,1, 1, −1, −3, −3}, {1, 1, 1, −3, 1, −3, 1, −3, −3, 1, −3, −3, 1, 1, −3,−3, −3, −3}, {1, 3, −1, −3, −1, 1, −3, −3, −1, −3, 3, −1, 3, 3, 3, 1,−3, −3}, {−3, 1, 1, −3, −3, 1, 1, −3, 1, −3, 1, 1, 1, 1, −3, −3, −3,−3}, {3, 1, 3, −1, 3, −3, 1, −1, −3, −1, −3, 3, −1, −1, 1, 3, −3, −3},{1, 3, −1, 1, 3, −1, −3, −3, −3, −3, 3, −1, −3, −1, 3, 1, −3, −3}, {1,3, 3, 1, 3, 3, 1, 3, −1, 3, −1, −3, −3, 1, 1, 1, −3, −3}, {1, 3, 1, 3,−1, 3, 3, 3, 3, −1, −3, 1, 1, −1, −1, 1, −3, −3}, {−1, 1, −3, 1, 3, −3,−1, −3, 3, −3, 3, 1, −1, −3, 3, −3, −3, −3}, {3, 1, −1, −1, 3, 3, −1, 3,−1, −1, 1, 3, −3, 3, −3, 3, −3, −3}, {1, 3, −1, 1, −1, 1, −3, −3, 1, 1,−1, −1, 3, 1, −3, 3, −3, −3}, {3, 3, 1, −1, −3, −3, −1, 1, −3, 1, 3, −3,−3, −1, −3, 3, −3, −3}, {1, −1, 1, −1, 3, −1, −1, −1, −1, 3, −3, 1, 1,3, 3, 1, −3, −3}, {3, −1, 1, −3, −3, 3, −1, −3, −1, 1, 3, 3, −1, −3, −1,−3, −3, −3}, {−3, 1, 1, −3, −1, 3, 1, 3, −3, 3, −1, −3, −1, −1, −3, −3,−3, −3}, {−3, 1, −3, 3, −1, 3, 3, 1, −1, 3, 3, 1, 1, 1, 3, −3, −3, −3},{−1, −3, −3, 3, 1, 3, −1, 3, −3, −1, 1, −3, 3, −1, −3, 3, −3, −3}, {−1,3, −1, −3, −1, −1, 3, 3, −1, −3, 3, 3, 1, 3, −3, −1, −3, −3}, {1, −3, 1,3, −1, −3, −3, −1, −1, −3, −1, −3, 3, −1, 1, 1, −3, −3}, {−1, −1, −3, 3,−3, −1, −3, 1, −3, −1, 1, −3, 1, 1, 3, 1, −3, −3}, {3, 1, −3, 1, −1, −3,3, −3, −1, −3, −1, 1, 3, −3, −1, −3, −3, −3}, {1, −1, 1, −1, −3, 1, −3,−1, 1, −1, 1, 3, 1, −1, 1, 3, −3, −3}, {1, −1, −3, 3, −1, 3, 1, −3, −1,3, −3, −1, 3, 3, 3, −3, −3, −3}, {−1, 1, −3, −1, 1, −3, 1, −1, 1, 1, −1,−3, 1, 1, 1, −3, −3, −3}, {−1, 3, 1, −3, −1, −1, 1, 1, −1, −1, −3, 3, 1,3, −3, 1, −3, −3}, {3, 1, 3, −1, 1, 1, −3, −1, 3, 1, −1, −3, 1, 3, 3, 3,−3, −3}, {−3, 3, 1, −3, 1, −3, −1, −3, −1, −1, −1, 1, 3, −3, −1, −1, −3,−3}, {3, −1, −1, −3, 1, −3, 1, −3, −3, −1, 3, 3, 3, 3, 3, 1, −3, −3},{1, −1, 3, 3, −1, −1, 3, −1, 3, 1, 3, −3, −1, −3, −1, −3, −3, −3}, {−1,1, −3, −1, −3, −3, 1, 1, −3, −3, 1, 1, 3, 1, −3, 3, −3, −3}, {−1, 1, 3,1, −3, 1, −3, −3, −3, 1, 1, −3, −1, −3, −3, −1, −3, −3}, {−1, 3, 3, 3,−3, −1, −3, 3, 1, −3, 3, −1, 1, −3, −1, −1, −3, −3}, {3, 1, 3, −1, −3,3, −3, −1, 3, −1, −1, −3, −1, −1, −1, 3, −3, −3}, {1, 3, −1, −1, 1, −3,−3, 3, −3, 3, −3, −1, −3, 3, 1, −3, −3, −3}, {1, 3, −3, −3, −1, −3, 1,−3, −1, 3, −1, −1, 3, 1, −1, −1, −3, −3}, {1, −3, 1, −3, −3, 3, 1, 3, 3,1, −1, 1, 3, 3, 1, 3, −3, −3}, {1, 1, 1, 1, −3, −3, 1, 1, −3, 1, 1, −3,1, −3, 1, −3, −3, −3}, {3, 1, −1, 3, 1, −1, 1, −3, 1, 3, −1, 1, 1, 3,−3, −3, −3, −3}, {−3, 1, −3, 1, −3, 1, 1, −3, 1, 1, −3, −3, −3, −3, 1,1, −3, −3}, {−3, 1, 3, −1, −1, 1, −1, 3, −3, 3, −3, −3, −3, −3, 3, 1,−3, −3}, {1, −1, −1, 1, −1, −1, 1, −1, 3, −1, 3, −3, −3, 1, 1, 1, −3,−3}, {1, 3, −3, −1, 3, −1, 1, −3, 3, −1, −3, 3, −1, −1, −1, −3, −3, −3},{−3, −1, 3, 3, 3, 1, 1, −1, 3, −1, 3, 1, −1, 3, 3, 3, −3, −3}, {−3, 3,−1, −3, 1, −3, 1, 1, 1, −3, 1, 3, −1, 1, 1, 1, −3, −3}, {1, −1, −1, 3,−3, 1, 1, −1, 1, −1, 1, −1, 1, −1, 3, 3, −3, −3}, {−3, −3, 1, 1, −3, −3,−3, −3, 1, 1, −3, 1, 1, −3, 1, −3, 1, −3}, {1, −3, 1, −3, −1, 3, 1, 3,3, −3, 3, 1, 3, 3, 1, 1, −3, −3}, {1, −3, 3, −3, 1, −3, −3, −1, −3, 3,1, −1, −1, −1, −1, 1, −3, −3}, {3, −3, 1, 3, 1, 3, −3, −1, −1, 3, 1, −1,1, −3, 3, −1, −3, −3}, {3, 1, −1, −3, 1, −3, 1, 3, 1, 1, −3, −1, 1, 3,−3, −3, −3, −3}, {3, −3, −3, −1, 3, −1, 3, −1, 1, 3, −1, −1, 3, 1, −1,−3, −3, −3}, {−3, 1, 1, −3, −1, −1, −3, 3, −3, 3, −1, 1, −3, 3, 3, −3,−3, −3}, {1, 1, 1, 1, −3, 1, −3, 1, −3, −3, 1, −3, −3, 1, 1, −3, −3,−3}, {3, −1, 3, −3, 3, −1, −1, −3, −1, 1, 3, −1, −1, −1, −3, 3, −3, −3},{−3, 1, −1, −3, −1, 3, 1, −1, 1, 3, −1, −3, −1, 1, −3, −3, −3, −3}, {3,−1, 1, 3, 1, 1, −3, 1, −1, 1, −1, 3, 3, 1, 1, 1, −3, −3}, {−3, 1, 1, −3,−3, −1, 3, −3, 1, −3, 3, 1, 3, 1, 3, −3, −3, −3}, {3, 1, 3, 1, −1, 1,−1, 3, −3, −1, 1, 1, −3, 3, 3, −1, −3, −3}, {−1, 3, 1, −3, −1, −1, 1, 1,3, 1, 3, −1, 1, −3, −1, −1, −3, −3}, {1, −3, 1, 3, −3, 3, −3, 3, 1, 1,1, 3, 3, −3, 1, 1, −3, −3}, {−1, −1, 3, −1, 1, 1, 1, −3, 1, 3, 3, −1,−1, −1, 1, −1, −3, −3}, {1, 3, −3, 3, −3, −1, −3, 1, −3, −1, −1, 3, 1,−1, −1, −1, −3, −3}, {−1, −3, 1, −1, 1, −1, −3, 3, 3, −1, 1, 3, 1, −3,−1, 3, −3, −3}, {3, −3, −3, −1, 1, −1, 3, −1, −3, 3, 1, −3, −1, 3, −3,−1, −3, −3}, {3, −1, −3, −1, 3, 3, −1, −3, −1, 1, 3, 1, 1, −3, −3, −1,−3, −3}, {−1, 3, −1, −3, −1, 3, 3, −3, 3, 1, −1, 3, 3, 3, −3, −1, −3,−3}, and {−1, 1, −1, 3, −1, −3, 1, 3, −3, 3, −3, −1, 3, 3, 1, −1, −3,−3}.

The sequence in the sequence set 1B includes some or all of thefollowing 388 sequences, and PAPRs of sequences {f_(n)} corresponding tothe sequences and equivalent sequences of the sequences are all greaterthan 2.6 dB but less than 2.7 dB:

{1, −1, 1, −3, 3, −3, 3, 1, −3, −3, −1, −1, −1, 3, −3, −1, −3, −3}, {1,3, 1, −3, 3, 1, 3, −1, 3, 3, 1, 1, 1, −1, 1, 3, −3, −3}, {1, −3, 3, −1,1, −1, −3, −3, 1, 3, −3, 1, −3, −3, 3, −3, −3, −3}, {3, −1, −3, −3, 1,−3, 3, 3, 1, 1, −3, −1, 3, 3, −3, 3, −3, −3}, {3, 1, −3, 1, −3, −1, 1,3, −1, 3, 3, −3, −3, −1, −1, −3, −3, −3}, {−1, 1, 1, −3, 1, −1, 1, 3,−1, 1, −1, −1, −1, 3, 3, 1, −3, −3}, {−1, −1, −3, 1, 3, 1, −3, 1, 3, −1,−1, 3, 1, −3, −3, −1, −3, −3}, {1, 3, −1, 1, −3, 3, −3, 3, 1, −3, −3,−1, −1, −3, 3, 3, −3, −3}, {−1, 3, −1, −1, −3, 1, −3, −1, −1, 3, −3, 1,1, 1, 1, 3, −3, −3}, {−3, 1, −3, 3, 1, −1, 3, −3, 1, 3, −3, −3, −1, −1,−1, −3, −3, −3}, {3, 1, 3, 1, −3, 3, 1, 3, 3, 3, −1, −1, 1, 3, −1, 1,−3, −3}, {1, 3, −3, 3, −1, 3, −3, 3, −1, −3, 3, −1, 1, 1, −1, −3, −3,−3}, {3, 1, −1, 3, −1, 1, 1, −3, −1, 3, −3, −3, 3, 1, 3, −3, −3, −3},{−1, −3, 1, −1, 3, −1, 1, 1, 1, −1, 1, −3, −1, 3, 1, 1, −3, −3}, {3, −1,1, −3, −3, 1, −3, 1, −1, 1, −1, −1, −1, −1, 3, 3, −3, −3}, {−1, −3, 1,−1, 3, −1, 1, 1, 3, −3, −1, −3, −1, 1, −1, −1, −3, −3}, {−1, 1, −3, 1,−3, 3, 1, −1, 3, −1, −1, −3, −3, 3, 3, −3, −3, −3}, {−1, 1, −3, 1, 3, 3,3, 1, −1, −3, 3, −1, −3, −1, −1, 3, −3, −3}, {−3, 1, −1, 3, 1, −1, 1, 3,3, −3, 1, −3, −1, 1, −1, −1, −3, −3}, {3, 3, −3, 3, 3, −3, 3, −1, −1, 3,−3, 1, −3, 1, −1, 1, −3, −3}, {−3, −1, 3, −3, 3, 3, 1, −3, 1, 1, 1, −3,3, 1, 3, 3, −3, −3}, {3, −1, −3, 1, −1, −3, −1, 1, 3, −1, 1, −1, 1, 1,1, −1, −3, −3}, {3, 1, −1, 1, 1, −1, −1, 3, −3, 1, 3, −1, −3, 1, 3, 3,−3, −3}, {3, −1, 3, −3, 1, 3, −3, 3, 1, 3, 1, −1, 1, 3, 3, −3, −3, −3},{3, 1, −3, 3, −3, 3, −3, 3, −3, 1, 3, −3, 1, 1, 1, 1, −3, −3}, {3, −3,1, −3, 1, 3, 1, −1, 3, 1, −3, 3, 3, −3, −1, −1, −3, −3}, {3, −3, 1, 3,−1, 3, 1, 1, −1, −3, 3, −3, 3, 1, 3, 3, −3, −3}, {−3, −1, 1, −3, −1, 1,1, 1, −3, 3, −1, −3, 1, −1, −1, −3, −3, −3}, {3, −1, −3, −3, 3, 1, −3,3, −1, −1, 1, 3, −3, 1, −3, −3, −3, −3}, {3, −1, 3, −1, 3, 1, −1, 1, 3,−1, −1, −3, 3, 3, 3, 3, −3, −3}, {1, 3, 1, 3, −3, −1, −3, 1, −3, 3, −1,−1, 3, 3, −1, −1, −3, −3}, {3, −1, 3, 1, −3, 3, 3, −3, −3, 1, −1, −1,−3, −1, 1, −3, −3, −3}, {−1, −1, −3, 3, 3, −1, 3, −3, 1, 3, 3, −1, 3, 1,−3, 3, −3, −3}, {−3, 1, 3, −1, 1, 3, 1, −1, −1, −3, 1, −3, 3, 1, 3, 3,−3, −3}, {−1, −1, 1, 1, −3, 3, −3, −1, 3, −3, −1, −3, 3, −3, 1, −1, −3,−3}, {−3, 3, 3, 1, 3, 1, −3, 1, 1, −3, −1, 3, 1, 1, 3, 3, −3, −3}, {−1,1, −3, 1, 1, 3, −3, 3, −1, −3, 3, −1, −1, −1, −1, −3, −3, −3}, {−3, 1,−3, −3, −1, 3, −3, −3, −3, −1, 3, 1, 3, 3, 1, −1, −3, −3}, {1, −1, 3,−3, −1, −1, 3, −3, 1, −3, 3, 3, 3, 1, −3, −3, −3, −3}, {1, 3, −3, 3, −1,−3, −3, 1, −1, −1, 1, −3, 1, −1, −1, −1, −3, −3}, {3, 3, 1, 1, −3, −1,−3, 3, −1, −3, 3, −3, −1, −3, 1, 3, −3, −3}, {3, −1, −1, 1, 3, 1, −3, 3,−3, −1, 3, −3, 1, −1, −1, −3, −3, −3}, {1, 3, 3, −3, 3, −1, 3, 3, −1, 3,3, 1, 3, 1, 1, −1, −3, −3}, {1, 1, 3, −3, −3, 3, −1, 1, −1, −3, −1, 3,−1, −3, −3, 1, −3, −3}, {1, −1, 3, 3, −3, −3, −1, 1, −3, −1, 3, −1, 1,−1, −3, −1, −3, −3}, {−1, −1, −3, −1, −1, 3, 1, −3, −3, 1, 3, −1, 3, 1,3, −1, −3, −3}, {3, 1, −3, 1, −1, 3, 3, −1, −3, −1, 1, −1, 1, 3, −1, −1,−3, −3}, {−1, 1, 1, 3, 3, −3, 3, 1, −3, 1, 3, −1, 3, 1, −1, −1, −3, −3},{3, −1, 1, −1, 1, 3, −3, −3, 1, −3, −3, −3, 1, −1, −3, −1, −3, −3}, {1,−3, −1, 3, −1, −3, 3, 3, −3, −1, −1, −3, −1, −1, 1, −1, −3, −3}, {1, −3,3, −1, −3, −1, 1, 1, 1, 3, −1, 1, 3, 1, −1, −1, −3, −3}, {−3, 3, 1, 3,3, −3, −1, −1, 3, 1, −1, 3, −3, 1, −3, −1, −3, −3}, {3, −1, 3, 3, −3, 1,−3, 3, 3, −1, −3, 1, 1, 1, 1, −1, −3, −3}, {−1, −3, 3, 3, −3, 3, −1, 1,3, 1, −3, 1, 3, 3, −1, 3, −3, −3}, {−1, 1, −3, 3, −1, 1, −1, −3, 3, 1,−1, 1, 1, −3, −3, −3, −3, −3}, {3, −3, −3, −1, −1, 3, −1, −3, −1, 1, −1,−3, 1, 3, −1, −1, −3, −3}, {−1, 3, −3, −3, 1, −3, −1, −1, 1, 1, −3, 3,−1, −1, −3, −1, −3, −3}, {1, 3, 3, 1, 3, 3, −1, −3, 1, −3, 1, −3, −1, 1,1, −1, −3, −3}, {−1, 3, 3, −1, −1, 1, −3, 1, −3, −1, −3, 3, 3, 3, 3, 3,−3, −3}, {1, −1, −1, 1, −1, −1, 3, −3, 1, −3, 1, −3, 3, 1, 1, 3, −3,−3}, {−3, 1, −3, −1, −3, 1, 1, 3, −3, −1, 3, 1, −1, −3, −3, −3, −3, −3},{1, 3, −1, 1, −3, 1, −1, 3, −1, −3, 1, 1, 3, 3, 1, −1, −3, −3}, {1, 3,3, 1, −1, 1, 1, −3, −1, 3, −1, 1, 3, 3, 3, 1, −3, −3}, {−1, 3, −3, −3,−1, 1, −3, −1, 3, 3, 1, −1, −3, 1, −3, −3, −3, −3}, {−3, 1, 3, 1, −1,−1, 1, −1, −3, 1, −1, −1, 1, 3, 1, 3, −3, −3}, {−3, 3, −1, 1, 3, 1, −3,−1, 1, 1, −3, 1, 3, 3, −1, −3, −3, −3}, {1, 3, −3, 1, −3, −3, −3, −1, 3,1, −3, 3, −3, 1, −1, −3, −3, −3}, {3, 1, 1, −1, −1, −3, −1, 1, −3, 1,−1, 3, −1, 1, 3, 3, −3, −3}, {−3, 1, 3, −3, −1, 3, −1, −3, 3, 1, −1, −1,−1, −3, 3, −3, −3, −3}, {3, −1, 3, 1, −3, 3, 3, −3, −3, −1, 1, −1, −1,−3, −1, 1, −3, −3}, {−1, 3, −1, 1, −3, −1, −1, −3, −3, 3, 1, 3, 3, −3,3, 1, −3, −3}, {3, 1, 1, 1, −3, −3, −1, 3, −3, −3, −1, −3, −1, 1, −3, 1,−3, −3}, {1, 3, −3, 1, 3, −3, −1, −3, 1, −3, 3, −1, −1, −1, 1, −1, −3,−3}, {1, −3, 3, 1, 3, 1, −1, 3, −3, −3, −1, 1, −1, 3, −3, −1, −3, −3},{1, −3, −1, −3, −1, 3, 1, 3, 3, −3, 3, −1, −3, 3, −1, −1, −3, −3}, {−3,1, 3, −1, −1, 1, 3, 3, −3, 3, −1, −3, −1, −1, −3, −1, −3, −3}, {−3, −1,1, −1, 3, −3, 3, −1, −3, 3, −1, 3, 3, −1, −1, −3, −3, −3}, {−1, 3, 3,−3, 1, 1, −3, −3, 3, −1, 1, −3, 1, −3, −3, −3, −3, −3}, {1, −1, 3, 3,−3, 1, −3, 3, 3, −3, −3, 1, 3, −1, 1, −1, −3, −3}, {1, 3, −1, 3, −3, 1,−1, −3, −3, 3, 1, 3, 3, −1, −3, 3, −3, −3}, {−1, 3, 3, −1, −1, 1, −3, 3,1, −3, 1, 3, −1, −3, −3, −3, −3, −3}, {−3, 1, −3, 1, 3, −3, 3, −1, −1,−1, −1, −1, −3, −3, 1, 1, −3, −3}, {−3, 3, −1, −3, −3, −3, 3, −1, 1, −3,−1, 3, −1, −1, 1, 3, −3, −3}, {−3, 1, −1, −3, 3, −1, 3, −3, −1, 1, 3, 3,3, −3, −1, −3, −3, −3}, {−3, −1, 3, −3, −3, −3, −1, 3, 1, −3, 3, −1, 3,3, 1, −1, −3, −3}, {−3, 1, −3, −1, 1, 3, −1, −3, 1, −1, −3, −3, 3, 3, 3,−3, −3, −3}, {1, −3, 1, 3, −1, 3, 1, −3, 3, 1, 1, −1, −1, 1, 3, −3, −3,−3}, {−1, 1, 1, −3, 1, −1, 1, 1, −3, 1, 3, −1, 3, 1, 1, −1, −3, −3},{−1, 3, −1, −1, −3, 3, −3, 1, 3, 3, −1, −3, 1, 3, 3, −3, −3, −3}, {−1,3, 1, 3, 1, −3, −3, 3, 3, −1, 1, −3, −1, −1, −1, 3, −3, −3}, {−1, 1, 3,−3, 3, 3, −3, −1, −1, −3, 3, −1, −3, −1, 3, −1, −3, −3}, {−1, 3, 3, 1,−1, 1, −3, −1, −3, 3, −1, −3, 1, 3, 3, −3, −3, −3}, {3, −3, 1, 3, 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−1, 3, −3, 1, 3, −3, −1, −3, 1, 1, −3, −3, −3}, {3, 1, −3, 1, −3,1, 1, −1, −3, 3, 3, −3, −1, 1, −3, −3, −3, −3}, {−1, 1, −3, 1, −3, 1, 1,3, −3, −1, −1, −3, 3, 1, −3, −3, −3, −3}, {−1, 1, 1, 1, −3, 3, −1, −3,−1, 3, −3, −3, 3, 1, −3, −1, −3, −3}, {3, −1, 1, −3, 3, 1, 1, −1, −1, 1,1, 3, 3, −1, −3, 1, −3, −3}, {−3, 3, 1, −3, 3, 1, 1, 1, −3, −1, 3, −3,1, 3, 3, −3, −3, −3}, {−1, −3, 3, −1, −3, 1, 3, −1, 1, −3, −1, −3, 3, 3,3, −3, −3, −3}, {−1, 1, −1, 3, 1, 3, −1, −1, 1, 1, −3, −1, 3, −1, −1,−3, −3}, {1, −1, −1, −3, −1, 3, −1, −1, 3, −1, −1, 1, −1, 1, 1, −3, −3},{3, −1, 3, −1, −1, −1, 1, 3, −3, 1, 1, −1, −1, −3, 3, −1, −3, −3}, {−3,3, 1, 3, −1, −3, −1, 3, −3, −1, 3, −1, −1, 3, 3, −3, −3, −3}, {−1, 1,−1, 1, −3, −1, 1, −1, −1, −1, 3, 3, 1, −1, 3, 1, −3, −3}, {−3, 1, −3, 3,−3, 1, 1, −1, −3, 3, −1, 1, 3, −3, −3, −3, −3, −3}, {1, −1, −3, −1, 3,−3, −3, 1, 3, 3, 1, −3, 1, 3, 3, 3, −3, −3}, {−3, −1, 1, −1, −3, −3, 1,3, −1, 3, −1, −3, 1, −3, 3, 3, −3, −3}, {3, −1, −1, 3, 3, 1, −3, −1, 1,−3, 1, −1, 3, −3, −3, −3, −3, −3}, {−1, 3, 1, −3, −1, 1, 1, 3, 3, 1, 1,−1, −1, 3, −3, 1, −3, −3}, {3, −1, 3, −3, −3, 1, −1, 3, 3, 3, −3, 3, 3,−1, −1, −1, −3, −3}, {−3, −1, −1, 3, −3, −1, −3, 1, −3, 3, 3, −3, 3, 3,1, −1, −3, −3}, {−3, −3, 1, −3, −3, 3, −3, 1, −3, 3, −1, 3, 1, 1, 1, 3,−3, −3}, {1, 3, −3, 1, 1, −1, −3, −3, −3, −3, −3, −1, −3, 1, −3, 1, −3,−3}, {−1, 3, 1, −3, −3, 1, −3, 1, 3, 1, 3, 3, 3, 3, −1, −1, −3, −3}, {1,−3, 3, −1, 3, −3, −1, −1, −3, 3, 3, −3, 3, 3, 1, 3, −3, −3}, {3, −1, 1,−1, 1, −3, −3, −1, −1, 3, 1, −3, 3, 3, 3, −1, −3, −3}, {1, −3, 3, −1, 1,−3, 3, 1, −1, 3, −3, −1, 1, −1, −1, −3, −3, −3}, {3, −1, −1, 3, 3, 1,−3, 1, −3, 3, −3, −1, −1, −1, −1, −1, −3, −3}, {1, −3, −1, −3, −1, −1,−3, −1, 3, 1, −3, 3, 3, −3, 1, 1, −3, −3}, {3, 3, −3, −1, −1, 3, −1, −3,1, −1, −1, 3, −1, 1, −3, −1, −3, −3}, {−1, −1, 3, 1, 3, −1, 3, −1, −3,1, 1, −3, −1, −3, −3, −1, −3, −3}, {−1, 3, 1, −3, −1, 1, 1, −3, −3, 1,1, −1, 1, −3, −3, −3, −3, −3}, {1, 3, 1, −1, −3, 1, −3, −3, 1, 3, −1,−3, 1, 3, 1, 3, −3, −3}, {3, 1, 3, −1, −3, 3, 3, 3, −3, −1, −1, 1, −1,−1, 3, −1, −3, −3}, {−1, 1, 1, 1, 1, −3, −1, 1, −3, −1, −3, 3, 3, −1, 3,1, −3, −3}, {1, −3, 3, −1, −3, 3, −3, 3, −3, −1, −1, −1, 1, 3, −1, −1,−3, −3}, {3, −3, 1, 3, −1, 3, 1, 1, 1, 3, 1, −3, 3, −1, 1, 1, −3, −3},{1, −3, −1, 3, −3, −1, −3, −1, −3, 3, 3, 3, 1, −1, 3, 3, −3, −3}, {−3,1, −3, −1, 1, −3, 3, 1, −3, −3, −3, 1, −1, −1, −1, −1, −3, −3}, {−1, −1,−3, −1, −1, −3, −1, 3, 3, −1, −3, 1, −3, 1, 3, 1, −3, −3}, {−3, 1, −1,3, 3, 1, −1, −1, −3, −1, 3, −3, 3, 3, −3, 3, −3, −3}, {3, −3, −1, 3, −3,1, −1, 3, 1, −3, 3, −3, −1, −1, −1, −3, −3, −3}, {−1, 3, −1, 3, −1, −3,−3, −1, −1, −1, −3, 3, 3, −3, 1, 1, −3, −3}, {1, −1, 1, −1, −3, 3, −3,1, −3, −1, 3, 3, −1, −1, 3, 3, −3, −3}, {3, −1, −3, 3, −1, 3, −1, −1,−3, −3, 1, −1, −1, −1, 1, −3, −3, −3}, {−3, 1, 1, −3, −3, −1, 3, 1, 1,−1, −1, 1, −1, 3, −3, 3, −3, −3}, {−3, 3, 3, 1, 1, −3, −1, −3, 1, −3,−3, −1, 1, −3, 3, 3, −3, −3}, {1, −3, −1, 3, 1, 3, −3, −3, 1, −1, −3, 1,−3, −3, −1, −3, −3, −3}, {3, −1, 3, −1, 3, −3, −3, 3, 3, 3, −3, −1, −1,−3, 1, 1, −3, −3}, {3, −3, 1, 1, −1, 1, −3, 3, −3, 1, −1, 3, 3, −3, −3,3, −3, −3}, {−3, −1, 3, −1, −3, 1, −3, −3, −1, 1, 1, 3, 3, 1, −1, −1,−3, −3}, and {−1, 3, −1, 3, −1, −1, 1, −1, 3, 3, −1, −1, 3, −3, −1, −1,−3, −3}.

A length of the sequence in the second sequence set is 24, PAPRs of{f_(n)} corresponding to the sequence in the second sequence set and theequivalent sequence of the sequence are all less than 2.8 dB, and thesequence in the second sequence set includes at least one of thefollowing: a sequence in a sequence set 2A, a sequence in a sequence set2B, and a sequence in a sequence set 2C. A PAPR of a sequence {f_(n)}determined by using the sequence in the sequence set 2C is less than2.45 dB.

The sequence in the sequence set 2A includes some or all of thefollowing 195 sequences:

{−1, −1, −3, −3, 3, −3, 1, 3, −3, 1, 1, −3, 3, 1, 1, −3, 3, −1, 3, 1, 3,3, −3, −3}, {−3, 3, 1, 3, −1, 1, −3, 1, −3, 1, −1, −3, −1, −3, −3, −3,−3, −1, −1, −1, 1, 1, −3, −3}, {3, −1, −3, 1, −1, −3, 1, 3, 1, 3, −3,−3, −3, −3, 1, 3, −1, −1, −1, −3, −1, −1, −3, −3}, {1, 1, 1, 1, −1, 3,1, 3, −1, −1, −3, 1, −3, 1, 1, 3, −3, 1, −1, −3, 1, 3, −3, −3}, {−1, −3,−1, 3, −1, 3, −3, −3, 3, 3, 1, 3, 3, −1, −3, −3, −1, 3, −3, −3, 1, 1,−3, −3}, {1, 3, −3, 3, 3, −3, −3, −1, −1, 3, −3, 1, −1, 3, −1, 3, 1, −1,−1, 1, −1, −1, −3, −3}, {1, 3, −1, 3, 1, 1, 1, −1, 3, −3, 1, 1, −3, 3,−1, −3, 1, 1, −1, 1, 1, 3, −3, −3}, {−3, −3, −1, 3, −3, −1, 1, −1, −3,1, −1, 3, 1, 3, 1, 3, −1, −3, −1, 1, 1, −1, −3, −3}, {1, −3, 1, 3, −3,3, 1, −1, −3, −3, −3, 1, −1, −3, 1, −3, −1, −1, 1, −3, −3, −3, −3, −3},{−1, 1, 3, −3, −1, −1, −3, 1, −3, 1, −1, 3, 1, 3, −1, −3, −3, 3, −3, 3,3, −1, −3, −3}, {−1, 3, −1, 1, −3, 1, −1, −1, −3, 3, −3, −3, 1, 3, 3,−1, −1, 3, 3, 3, 3, −3, −3, −3}, {−3, 3, −1, 1, −1, −3, −3, −3, 3, −3,−3, −3, 1, −1, −1, 3, −1, −1, 3, −1, 1, 3, −3, −3}, {−1, 3, 1, −3, −1,3, 1, −3, −1, −1, −3, 1, −1, 1, 3, −3, 3, −3, −1, 1, −1, −1, −3, −3},{1, 1, −3, −3, −3, 3, −1, −1, 3, 1, 1, −3, 1, −3, −1, 3, −3, −3, −1, −3,−1, −3, −3, −3}, {−1, 1, 3, −1, 3, −3, −1, 3, 3, −3, −3, −3, 3, −3, 3,−1, 1, −1, −3, 3, 1, −3, −3, −3}, {−1, 3, 3, 1, 1, −1, −1, 1, −3, 1, −3,−1, 3, 1, −3, −3, 1, 1, 3, 3, −3, 3, −3, −3}, {3, −1, 3, −3, 1, −1, 3,−1, 1, 1, −1, 3, 1, 1, 3, −3, −3, −1, 1, 1, −1, −1, −3, −3}, {−3, −1, 1,−3, −3, −1, −1, −3, −3, −3, 1, −3, 1, 3, 1, −1, −1, −3, 1, 1, 3, 1, −3,−3}, {−3, 1, −1, −3, 1, −1, 1, −3, 1, −3, 3, 1, 1, −1, −1, −3, −1, −1,−3, −1, 1, 3, −3, −3}, {1, −1, −3, −3, 3, 1, −3, 1, 3, −1, −1, 1, 3, −3,−3, 1, −3, 3, 3, −3, 3, −3, −3, −3}, {−1, 3, −3, −3, −3, −3, 3, −1, 3,3, −1, −3, 1, −3, −1, 1, 1, −3, 3, 3, 1, 1, −3, −3}, {3, −3, 3, 1, −3,−3, 3, −3, −3, 3, 3, −1, 3, −1, 3, −1, −1, −3, −1, 1, 1, 3, −3, −3},{−1, −1, −3, −3, −1, −3, 3, −3, 3, −1, −1, −3, −3, 1, 1, −3, 1, −1, 1,3, 1, 3, −3, −3}, {−3, 1, −1, −3, 3, −1, −3, −1, 3, 3, 3, 3, −3, 1, 1,−3, −1, 3, 3, 3, −3, −1, −3, −3}, {3, 1, 3, 1, 3, 3, 1, −3, 1, −3, 3, 3,3, −3, −1, −1, 3, 1, 1, −3, 1, 1, −3, −3}, {1, −1, −3, 1, −3, 1, −3, −3,1, −1, 3, −3, 1, 3, 3, −3, 3, 3, 1, 1, 3, −3, −3, −3}, {−1, −1, 3, −1,3, −3, −1, 3, −1, 3, 1, −3, −1, −1, −1, −3, −1, −1, 3, 3, 1, −1, −3,−3}, {3, −3, −3, −1, 1, −1, 3, −1, 1, 1, −3, 1, 1, −3, 1, 1, −1, 3, 1,1, −1, −1, −3, −3}, {1, 1, 1, 3, 3, −3, 1, −3, 1, −3, 3, −3, 1, 1, −3,−1, −1, 3, −1, −3, 3, 1, −3, −3}, {1, −1, −1, −3, 1, −1, −3, 1, 3, −1,−3, −1, 3, −3, 1, 1, 3, −1, 1, 1, 1, 3, −3, −3}, {3, −1, −3, 1, −3, 1,1, −3, 1, −3, −3, 3, 1, −1, 1, 3, 3, −3, −1, −3, −3, −3, −3, −3}, {−3,−3, −1, 1, 1, −3, 3, −3, −3, 1, 3, −1, −1, 3, 3, 1, −3, 1, −3, −1, −3,−1, −3, −3}, {−1, 3, −1, −1, −1, −1, 1, −1, 1, 3, −1, −1, −3, −3, 3, 1,−3, 3, 3, −1, 1, 1, −3, −3}, {−3, 1, −1, 1, −1, −1, −3, −1, −3, −1, 3,1, −1, −3, −1, 1, −1, 1, 3, −3, 1, 3, −3, −3}, {3, 1, −3, −3, 1, −1, 3,−1, −3, 3, −3, −1, −1, −3, −1, 1, 3, −1, 1, −1, 1, −3, −3, −3}, {1, −1,1, −1, 1, −3, −1, −1, −3, 1, 3, −3, −3, 1, −1, 3, −1, −1, 3, 3, 3, 1,−3, −3}, {1, −1, 3, 1, −3, 1, −1, −1, 1, 3, −3, −1, 1, −1, −1, 1, 1, 1,−3, 1, 3, −1, −3, −3}, {1, −1, −3, 3, 1, 3, 1, −1, 3, −1, 3, −3, −3, 1,−3, −1, −3, −1, −1, −1, 3, −3, −3, −3}, {−1, −3, 3, −1, −1, −3, −1, 1,3, −1, −1, 1, 3, −1, 3, −1, 3, −1, −1, 1, −1, −3, −3, −3}, {3, −1, 3,−1, 3, −3, −1, 3, 3, −1, −1, −1, −3, 3, −1, −1, −1, 1, 1, −3, −3, −3,−3, −3}, {−3, −3, 1, −3, −1, 3, −1, 3, 1, −3, 1, −1, −3, −1, −1, 3, −3,−1, −1, 1, 1, −1, −3, −3}, {1, −3, 3, −3, 1, −3, 1, 3, 1, −1, −3, 1, 3,3, 3, 3, −1, 3, 3, −1, 1, 1, −3, −3}, {3, −1, 3, −1, −3, −1, −1, −1, −3,−3, 3, 3, −1, −3, 1, 1, −3, 3, 3, −1, 1, 3, −3, −3}, {1, −3, −3, −1, 3,−1, 1, 3, 1, −1, 1, −1, 3, 3, 1, −1, 1, 1, −1, 1, 1, 1, −3, −3}, {−3,−1, −3, 3, 1, 1, −3, −3, −1, 3, −3, 1, −1, 1, 3, −1, 3, −1, −3, 3, −3,−3, −3, −3}, {−3, 1, −3, −1, −1, 3, −1, 1, −1, 1, 3, 3, −3, −1, 3, 1,−1, 3, 1, −1, −1, −1, −3, −3}, {3, 3, 3, −1, −1, 1, 3, −1, −1, −1, −3,1, −1, −3, −1, −3, −1, 3, 1, 1, −3, 1, −3, −3}, {3, −3, 3, −1, −1, 1, 1,3, 1, 1, −1, 3, −1, 3, −1, −3, 3, 1, 1, −3, −1, 1, −3, −3}, {3, −1, −1,−3, −3, 1, −1, 1, −1, −3, 1, −3, 3, −3, 1, 1, 1, 3, 1, −3, −1, 1, −3,−3}, {3, −1, −3, 1, 1, −3, −3, 1, 3, −1, 3, −1, 3, −3, −3, 1, −1, −1,−1, −3, −3, −3, −3, −3}, {−3, 3, −1, −3, 1, 1, −3, 1, −3, −1, −1, 1, −1,−1, −1, 3, 1, 1, −1, −1, 3, −3, −3, −3}, {3, 1, −1, −3, 3, −1, 3, 3, −1,−1, 1, −3, 3, −3, 3, −1, 1, 3, −3, 3, −3, −3, −3, −3}, {−1, 3, 1, −1,−3, 3, −3, −1, 3, −1, 1, −3, −3, −3, 3, −1, 1, −1, −3, −1, −1, 1, −3,−3}, {1, −3, 1, −3, −3, 1, −1, 3, −3, −1, 1, 3, 1, −3, −3, −3, 1, −1,−1, −3, −3, −3, −3, −3}, {1, −3, 1, 3, −3, −3, 1, −1, 1, −1, 1, 3, −3,3, 1, 1, −1, −3, −3, −1, −1, −3, −3, −3}, {−3, −1, −1, 1, −3, −1, −1, 1,−3, 1, 1, −3, 1, 3, −1, −1, −3, 1, 1, 1, −1, −3, −3, −3}, {1, −3, 3, −1,3, −3, −3, 1, −1, −3, −3, 1, −3, 1, 1, −1, −1, −1, −1, 1, 3, −3, −3,−3}, {−1, −1, 1, 1, 1, −1, −1, 3, −3, 1, −1, −1, 3, −1, 3, 1, 3, −1, 1,−1, −3, 1, −3, −3}, {−1, −3, 1, −1, 3, 3, −1, 1, −1, −1, −1, −1, −3, −3,1, 1, −1, −3, 1, 3, 1, 3, −3, −3}, {3, 3, 3, 3, −1, −3, 3, −1, 3, −3, 3,3, −3, 1, −1, 1, −1, 1, −3, −1, 1, 1, −3, −3}, {1, −3, 1, 3, −1, −1, −1,−3, 3, 3, −3, −1, −1, 3, −1, −3, 1, 1, −3, −3, 3, −3, −3, −3}, {3, 1,−1, −3, 1, −1, 1, −1, 3, −1, 3, −1, 1, 3, −1, 1, 3, 3, −3, −1, −1, −1,−3, −3}, {−1, −3, −1, −3, −1, 3, 3, 3, 3, −3, −3, −3, 1, 1, −3, −3, −3,1, −1, −3, 1, −3, −3}, {−3, 1, −1, 1, 3, −3, −1, 3, 1, 3, −3, 1, −1, −3,−1, 3, 3, −1, −3, −3, −3, −1, −3, −3}, {3, 3, 1, −3, −1, −1, 1, −1, 3,−1, 3, −3, 3, −3, −3, 3, −1, −3, 3, −3, −1, 1, −3, −3}, {1, 3, −1, 3,−1, 1, −1, 3, 1, −3, −1, 1, 3, −1, 1, 1, −1, −3, 3, 3, 3, 3, −3, −3},{1, −3, 3, −1, −3, 1, −3, −3, −3, −1, −1, 3, −3, 1, −3, −1, 3, 1, 1, −1,−3, −3, −3, −3}, {−1, 1, 1, 3, −3, −1, −1, −3, 3, −1, 1, −3, −3, 3, 3,−3, 3, 3, −1, 3, −1, −3, −3, −3}, {−1, −3, 1, 3, −3, −1, 1, −3, 3, −1,−3, 3, 3, 1, −1, −1, 3, −1, 3, −3, −3, −3, −3, −3}, {−1, 1, 3, −1, −1,3, −3, −1, −3, −1, 3, −1, 3, 1, −3, 3, −3, 3, 1, −1, −3, −3, −3, −3},{−3, −1, 3, −1, −3, 1, −3, −1, −1, 1, 1, −3, 1, −1, −1, 3, −1, 1, 1, −1,−3, −3, −3, −3}, {1, 3, 3, −3, −1, 3, 1, −3, −1, 1, −3, −1, 3, 3, −1, 3,−3, 3, 1, −1, −3, −3, −3, −3}, {1, 1, 1, 1, −3, −3, −1, −3, 3, −1, 3,−3, 3, 1, −3, −1, 3, −3, 3, −3, 1, 3, −3, −3}, {−1, 3, −1, −3, 1, −1, 1,−3, 1, 3, −3, −3, −3, 3, −1, −1, 3, 3, −1, −1, −1, −1, −3, −3}, {−1, 3,3, 1, −1, −1, 3, −1, 3, −1, 3, 1, −1, 1, 1, −1, 1, 1, −1, 1, 3, −3, −3,−3}, {1, −3, −1, 3, −1, 3, 1, −1, −3, −1, −3, 3, −3, 3, −1, −1, −1, 1,−1, −1, 1, 3, −3, −3}, {−1, 1, −3, −3, −3, 1, 1, 1, 1, 3, 1, 3, −1, 3,−1, −3, 3, −1, −3, 3, −1, 1, −3, −3}, {−1, 3, −1, −1, 3, −1, −1, 3, −1,−1, −1, 3, 3, −1, 1, −1, 1, −1, 1, 1, 1, −3, −3, −3}, {3, −1, −1, 3, −1,3, 3, 1, −1, 3, −1, 3, −1, 3, 3, 1, 1, 1, 3, 1, 1, 3, −3, −3}, {1, 3,−1, −3, 1, −1, −3, −3, −1, 3, −3, 1, 3, 3, −1, −1, −3, 3, 3, 3, −3, −3,−3, −3}, {−1, −1, −3, 1, 3, 1, 3, −3, −3, −3, −3, 3, 3, −3, 3, 1, −3, 1,−3, −3, −1, 1, −3, −3}, 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1, 3, 3, 1, 3, −1, −1, −3, −1, −3, 3, −3, −3, −3, 3,1, −3, −3}, {−3, 1, 3, −3, 3, −3, 3, −3, 3, −3, −1, −1, 1, 1, −3, −3, 3,−1, 3, 1, −1, 1, −3, −3}, {3, 1, 1, −1, −3, −1, 1, −3, 3, −1, 3, −1, −3,3, 1, 3, −3, 1, 3, 3, 3, −3, −3, −3}, {1, −3, 3, −1, 1, 3, 3, 1, −1, 1,1, −1, 3, −3, 3, 1, −1, −1, 3, −3, 3, 3, −3, −3}, {3, 3, −3, 3, −3, 3,−1, 3, −1, 1, −1, −1, −3, 3, 3, −1, −1, −3, 1, −3, −3, 1, −3, −3}, {−3,1, −1, 3, −1, 3, 1, 1, −3, −3, 1, −3, −1, 3, −3, −3, −3, 1, −1, −1, −3,−3, −3, −3}, {−1, 3, 1, −1, −3, −1, 3, 1, 3, −3, −1, −3, 1, −3, −1, 3,3, −3, 1, −3, −3, −3, −3, −3}, {1, −1, −3, 1, 3, −3, −1, 3, −3, 3, 1,−3, 3, −1, −1, −1, 3, −3, 3, −3, 3, −3, −3, −3}, {−1, 1, 3, 3, −1, 1,−3, 1, 3, −1, 3, 3, 1, −3, 3, −1, −3, 1, −1, −1, −1, −3, −3, −3}, {3, 1,−1, 3, −1, −1, 1, −3, −1, 3, 3, −3, −1, −3, 1, 3, −3, 3, −3, 1, −3, −3,−3, −3}, {3, 1, −1, 3, −1, −1, 3, −1, 3, −1, 3, 1, 3, −1, 1, 3, −3, −1,−1, 1, 1, −1, −3, −3}, {−3, −3, −1, −1, −3, −1, 1, −3, 1, −3, −3, 3, 3,−1, −3, 3, 3, −3, 1, −1, 1, −1, −3, −3}, {3, 3, 3, −3, −3, 1, −1, −3, 1,−3, −3, −1, 1, −3, −1, 1, −1, 3, −3, 1, −1, −1, −3, −3}, {−3, 1, 3, 1,−3, −1, 3, 1, −3, −3, 3, 3, −3, 3, −1, −3, 3, −1, 1, 1, −1, 1, −3, −3},{1, −1, 1, −1, −1, −3, 1, 3, 1, −1, 3, 1, 3, −1, 1, −3, −3, 1, −1, −1,1, 3, −3, −3}, {1, 1, 1, 3, −3, 3, 3, 3, 3, −1, −1, 3, 1, 3, −1, 3, −1,−1, 1, −3, −3, 1, −3, −3}, {−1, 1, −3, 1, −3, −1, −3, −1, 3, 3, −3, −1,−1, 1, −1, 3, 1, −1, 3, 3, −1, −1, −3, −3}, {−3, −1, 1, −3, −3, 3, 1, 1,−1, 3, 1, 3, −3, −3, −1, −3, 1, −3, 3, −3, −3, 3, −3, −3}, {−1, 3, −3,3, −1, 1, −3, −3, 3, −1, 1, 3, 3, 1, 3, 3, 1, −1, 3, −1, −3, 3, −3, −3},{−3, 1, −3, 1, −3, 3, −3, −1, −1, 1, 3, −1, 1, −3, −1, 1, −3, 3, 1, −1,−3, −3, −3, −3}, {−1, 3, −1, −3, 1, −3, 3, 3, −3, −1, 1, −1, −1, −3, −3,−3, −1, 1, −3, −3, 3, 1, −3, −3}, {1, 3, 3, 3, 3, 3, −1, 1, −3, 1, −3,1, −1, −3, −1, −3, 3, 1, −3, −3, 1, 1, −3, −3}, {1, 1, −1, −1, −3, 3,−3, −3, −3, 1, −3, 3, −3, −3, −1, 3, 1, −3, 1, 3, −3, 1, −3, −3}, {−3,−1, 1, −3, 1, −1, 3, 1, −3, 1, 3, 1, −3, −3, 3, 1, −3, −1, 1, −1, −1,−3, −3, −3}, {−3, −3, 3, −3, −3, −3, −3, 1, −3, −1, 1, 1, −1, −3, 1, 3,−3, −3, 1, −1, 1, 1, −3, −3}, {3, −3, −3, 3, −3, 3, −3, 1, −1, −3, 1,−1, −3, −3, 1, −3, −1, −3, 3, 1, 1, 3, −3, −3}, {1, 3, −1, −1, 3, −1, 3,1, −3, −3, −1, 1, −3, 3, 1, 1, −3, 3, −3, −1, −3, −3, −3, −3}, {−3, 3,−3, −3, −1, −3, 1, −1, −1, 1, 3, −3, 1, 1, 1, −3, 1, −3, −1, 1, 1, −1,−3, −3}, {−3, −1, 3, −1, 1, −1, 1, 1, 3, −1, −3, 3, 1, 1, −3, −3, −1,−1, 3, −1, −1, −3, −3, −3}, {1, −1, −1, −3, −1, 3, −3, −1, −1, 3, −3,−1, 3, 1, 3, 1, −3, 1, −1, 3, 3, 3, −3, −3}, {−1, −1, −3, −3, −3, −1,−1, −3, 1, 3, 1, 3, −3, 3, −1, 3, −3, 3, 1, −3, 1, 1, −3, −3}, {−1, 3,1, 3, 1, −1, −3, −1, −3, −3, 1, 3, −3, 1, 3, −3, −3, −1, −3, −3, 3, −1,−3, −3}, and {−3, 3, 1, −1, 1, −1, −3, −1, 3, −3, −3, −1, 1, 3, −3, 3,3, −1, 3, −3, 3, −3, −3, −3}.

The sequence in the sequence set 2B includes some or all of thefollowing 88 sequences whose PAPRs are less than 2.6 dB:

{−1, −3, 1, −1, 3, −1, 3, −1, 1, 3, 1, 1, −1, −1, −1, −1, −1, 1, 3, −3,1, 1, −3, −3}, {−1, −3, 3, 1, 1, −3, 1, −3, −3, 1, −3, −1, −1, 3, −3, 3,3, 3, −3, 1, 3, 3, −3, −3}, {1, 3, −3, −1, 3, −1, −3, 1, −3, −1, 1, 1,3, 3, −1, −3, 3, 1, −1, −1, −3, −3, −3, −3}, {−1, 3, −1, 1, −3, 1, 1,−3, 3, 1, 1, 3, 3, −3, 1, −1, 3, 1, 1, 1, −1, −3, −3, −3}, {1, −1, −3,1, 1, −3, −3, 3, 3, −3, 3, −1, 3, −1, −1, −3, −3, −3, −1, 1, −1, 3, −3,−3}, {3, −1, 1, −3, 3, −1, 1, −1, 3, 3, 1, 1, −3, −1, −1, −3, 3, −3, 3,3, −3, 3, −3, −3}, {1, −1, −1, −1, 3, 3, 3, −3, −3, 1, −3, 1, −3, −3, 1,−3, −3, 1, −3, −3, −3, 1, −3, −3}, {3, −3, 3, 3, 3, 3, 3, −3, −1, 1, −3,−3, 3, 1, 3, −1, −3, 1, −1, 3, 1, 1, −3, −3}, {−1, −3, 3, −1, 3, 1, 3,−1, 1, −3, −1, −3, −1, 1, 3, −3, −1, −3, 3, 3, 3, −3, −3, −3}, {−1, 1,−3, −1, 3, 3, 1, 1, −1, 3, −1, 1, −1, −3, −1, 1, 1, −3, 3, −1, −3, 3,−3, −3}, {3, −1, 3, −1, 1, −3, 1, 1, −3, −3, 3, −3, −1, −1, −1, −1, −1,−3, −3, −1, 1, 1, −3, −3}, {−1, −1, 1, 1, −1, −1, 1, 3, −3, −3, 3, −1,−1, 3, −3, 3, 3, −1, 1, −3, 1, −3, 1, −3}, {−1, −3, 3, 1, −1, −1, 3, −1,3, 3, −3, 1, −3, 1, −1, 1, 3, −3, −3, −1, −3, −3, −3, −3}, {−1, −3, 1,−1, −3, 1, −1, 3, −3, 1, −1, 1, −3, −1, 1, 3, −1, 1, 1, 1, 1, −3, −3,−3}, {3, −1, 1, −1, 3, −3, 1, −1, 1, −1, −3, 1, −3, 3, 1, 1, 3, −3, −1,−3, −3, −1, −3, −3}, {3, −1, 1, 3, −1, 1, −3, 3, −1, 3, 1, 1, −1, 3, 1,1, 1, −1, −1, 1, 1, 3, −3, −3}, {1, −1, 1, −3, 3, 1, 3, −1, −3, 3, −1,−3, 3, 1, −3, −1, −1, −1, −3, −1, 3, −3, −3, −3}, {−1, 3, 1, −1, 1, 3,3, 3, −1, −3, 1, 3, −3, 1, −3, −1, 1, 1, −1, −3, −1, −3, −3, −3}, {3,−3, 1, −3, −1, −3, 1, 1, −3, −1, 3, 3, −1, −1, 3, 1, −3, −3, −1, −1, −3,−3, −3, −3}, {3, −3, −1, 1, −1, 1, −3, −1, 3, 1, 3, 1, −3, 1, −1, −3,−1, −1, −3, −3, 1, −1, −3, −3}, {1, −1, 1, −1, −3, 1, −3, 1, 3, −1, 3,3, −1, −1, 3, −3, −1, −1, 3, 3, 3, −3, −3, −3}, {1, 3, 1, −3, 3, 1, −3,3, −1, 1, −1, 1, 3, 3, 1, 3, −1, 1, 1, 3, −1, −1, −3, −3}, {3, 1, −3,−1, 1, −3, 3, 1, 1, −1, −3, −3, −1, −1, 3, 3, 3, 3, −3, 3, −3, 3, −3,−3}, {3, −1, −1, 3, −3, 1, −3, 1, −3, 3, 3, −1, 1, 1, −3, −3, 3, 1, 3,3, 3, 3, −3, −3}, {−3, 3, 1, 1, −3, 1, −1, 1, −1, 3, −1, −1, 1, −3, −1,1, −3, 1, 1, 1, 3, −3, −3, −3}, {1, −1, −1, 1, 1, −1, −1, −1, 3, 3, 1,1, 3, −3, −3, −1, −3, 1, 1, −3, 1, −3, 1, −3}, {−1, 3, 1, −3, 1, −1, −3,1, 1, −1, −3, −1, 1, −3, −1, 1, 1, 1, 3, −3, −1, −3, −3, −3}, {−3, 3,−3, 3, −1, 1, 1, 3, −1, 1, 3, −3, 3, 1, 3, 3, 1, −3, −1, 3, 3, 1, −3,−3}, {3, −1, 1, −1, 3, −3, 1, 1, 3, −1, −3, 3, 1, −3, 3, −1, −1, −1, −1,1, −3, −3, −3, −3}, {3, −3, −1, 1, 1, 3, −3, −1, −3, −3, 1, −1, 3, 1, 1,−1, −3, −3, 3, −1, −3, −1, −3, −3}, {1, 1, −1, 1, −1, 1, −3, 1, −1, −3,3, 1, 1, −3, −1, 3, 3, −1, 1, 1, 1, 3, −3, −3}, {3, −3, 1, −3, 1, 1, −1,1, 1, 3, 3, −3, −3, 1, 1, −3, −1, −3, −3, −3, 1, −1, −3, −3}, {1, −3, 1,−3, 3, −1, 1, −1, 1, 3, 1, 3, −3, −1, −3, 3, 1, −1, −3, −1, −1, −3, −3,−3}, {−1, −3, −3, 3, 3, 1, −3, 1, 1, 1, −3, 1, −3, 3, −1, 1, 3, −3, 1,3, 3, 3, −3, −3}, {3, 1, −1, −1, −3, 1, −3, 1, −3, −1, 3, −3, −1, 3, 3,−3, 1, 1, 3, 3, −3, −3, −3, −3}, {−1, 1, −3, −3, −1, 1, 1, 3, 1, −3, −1,3, −3, 1, 3, 1, −1, −3, 3, −1, −3, −1, −3, −3}, {3, −1, 3, 3, 1, −1, −1,3, −1, −1, 3, −1, −3, 1, −1, 1, −1, −1, −1, 1, 1, 3, −3, −3}, {−1, 1, 3,−3, 1, 1, −3, 1, −1, −3, 1, −1, −1, −3, 3, 1, 3, −1, 3, −1, 3, −3, −3,−3}, {1, −1, −3, 3, 3, 1, 3, −1, −1, 3, −3, −1, −1, 3, −1, −3, −1, −1,−1, 1, −3, 3, −3, −3}, {3, −1, 1, −3, 1, 3, −1, −3, 1, −1, −3, −1, −1,1, 3, 3, −3, 3, 3, 3, 1, 1, −3, −3}, {−3, 1, 3, −1, 3, 3, −3, −1, −3, 3,−3, −3, 3, −3, 3, −1, −3, 3, 1, 1, 1, 1, −3, −3}, {1, −3, −3, 3, −3, −1,−3, −1, 1, −3, −3, −3, 3, −3, 1, 1, 1, −3, 3, −1, 3, 1, −3, −3}, {3, −3,1, −3, 1, 1, 3, 1, −3, 1, −3, −3, −1, 1, 3, −1, −3, 3, 1, −1, −3, −3,−3, −3}, {1, −3, 1, −1, 3, −1, −1, 3, −3, −1, 3, 1, 3, −3, 3, 3, −3, −3,3, 1, 1, −3, −3, −3}, {1, −3, −1, 3, 1, −3, −1, 3, −1, −3, 3, −1, 3, 1,1, 3, −3, −3, −3, −1, −1, −3, −3, −3}, {3, 1, −3, 3, −1, 3, 1, 3, −3, 3,−3, −1, 1, 1, −3, 3, 3, 1, 3, −3, −1, −1, −3, −3}, {−1, 3, −3, −1, −3,1, 3, −3, 1, −1, −3, 3, 3, 1, −1, 3, −1, 1, 1, 3, 1, 3, −3, −3}, {1, −3,3, −1, −3, −1, 3, 3, 1, −1, 1, 1, 3, −3, −1, −3, −3, −3, −1, 3, −3, −1,−3, −3}, {−1, 3, −1, 3, −1, −1, −3, −1, −3, 1, 3, 3, −1, 1, −1, −1, 3,3, −1, −3, 3, 3, −3, −3}, {3, 1, 3, 1, 3, 1, −3, 1, 3, −1, 3, −3, −1, 3,−3, −3, 1, 1, −1, −1, 3, 3, −3, −3}, {−1, 3, −1, 3, −1, −1, −3, 3, −1,1, 3, −1, −1, −1, 1, 1, −1, 1, −1, 1, 1, −3, −3, −3}, {−3, −1, 1, −3,−3, 1, 1, −3, 3, −1, −1, −3, 1, 3, 1, −1, −3, −1, −3, 1, −3, −3, −3,−3}, {3, −1, 1, −1, −1, 3, −3, 3, −1, 3, −3, 3, 1, −3, −3, 3, −1, −3,−3, −1, −1, 3, −3, −3}, {1, −1, 1, 1, 3, 1, 3, −3, −1, 3, −1, −3, −1,−3, −3, −3, 3, 3, −1, −3, 1, 1, −3, −3}, {3, −3, 1, 1, 1, −3, 3, −1, 1,3, 1, −1, 3, −3, 1, 1, 1, 1, −3, 3, −3, −3, −3, −3}, {−1, −1, 1, 3, −3,3, 1, 3, −1, 1, −1, 3, −1, −3, 3, −1, 1, −3, −3, 3, −3, −1, −3, −3},{−1, 3, −3, 1, −3, 3, 3, 3, −3, 1, 1, −1, −1, 3, 3, 3, 1, −3, 3, −1, 3,3, −3, −3}, {−3, −3, −1, 3, 3, −3, −1, 1, −1, 1, 1, 1, −3, 1, −3, −3, 1,−3, −1, 3, 1, −1, −3, −3}, {3, −3, 3, −3, −3, 1, −1, 1, −1, −1, −3, −3,1, −3, −1, −3, 3, 3, −1, −3, 1, 3, −3, −3}, {1, −3, 3, −3, 3, −1, −1,−3, −1, 1, 3, 3, −1, −1, 3, 3, −1, −1, −3, −1, −3, −3, −3, −3}, {3, −3,3, −1, 3, −1, −1, −3, −3, −1, 3, −3, 1, −3, −3, 3, 1, −1, −3, 1, 3, 3,−3, −3}, {−3, 1, −3, 1, −3, −3, 1, −3, 1, −3, −3, −3, −3, −3, 1, −3, −3,1, 1, −3, 1, 1, −3, −3}, {−1, −1, −3, 3, −3, 3, 1, −3, 1, 3, −1, 3, −3,−1, −3, −3, −1, −1, −3, −1, 1, 1, −3, −3}, {−3, −1, 1, 3, −1, 3, 3, −3,−1, −3, 1, 3, −3, 3, −1, 3, 3, 3, 3, 1, −1, −3, −3, −3}, {1, 1, 1, 3, 3,1, −3, 3, 1, −1, −1, −1, −3, −3, 1, 3, −3, −1, 1, −3, 1, −3, 1, −3},{−3, 3, 1, −1, −3, 1, −3, 1, 1, −1, 1, −3, −1, −3, −1, 3, 3, −3, 1, 3,3, −3, −3, −3}, {−1, 3, −3, 3, 3, 1, 1, −3, −1, −1, 1, −3, 3, −1, 3, −3,−3, 3, 1, −3, 3, 3, −3, −3}, {1, −3, 3, 1, −3, 1, 3, −1, −3, 3, −1, 1,−3, −3, −3, 1, 3, −1, 1, 1, 3, −3, −3, −3}, {−3, 1, −1, 1, −3, −3, −1,−3, 1, −1, −3, −3, −1, −3, 3, 1, 1, 1, 3, −3, 1, −3, −3, −3}, {−3, 1,−3, 1, −1, 1, −3, −1, 3, −3, −1, −3, 3, 1, −1, 1, 3, −3, −3, 3, 3, 3,−3, −3}, {1, −3, −3, 1, −1, −1, 3, −1, 3, 3, 3, 3, −1, −3, 1, −3, −1,−3, −3, −3, 1, 3, −3, −3}, {−1, 1, 3, 1, −1, 1, 1, −1, −3, −1, −1, 1,−3, 1, 3, −1, −1, 3, 1, 3, 1, −3, −3, −3}, {−3, 3, 1, 1, 1, −3, −3, 1,−3, 3, −1, 1, −1, 3, −1, 1, −3, −1, 1, −3, 3, −3, −3, −3}, {3, −3, −3,−1, 3, 3, −3, −1, 3, 1, 1, 1, 3, −1, 3, −3, −1, 3, −1, 3, 1, −1, −3,−3}, {−3, 1, −1, 3, 1, −3, 1, 3, −3, −3, −1, 3, −3, 1, 1, −3, −3, 3, −1,−1, −3, −3, −3, −3}, {3, −1, 3, −1, 1, −3, 3, 1, 3, 3, −1, 1, −1, −1, 1,1, 3, −3, −3, 3, 3, 1, −3, −3}, {3, −3, 1, −1, 1, −1, 1, −1, 1, −3, −1,1, −3, 1, −1, −3, 1, −1, 3, 3, 1, 1, −3, −3}, {−3, −1, 1, 3, −3, 1, −3,−1, 3, 1, 1, −3, 3, −3, 3, −1, −3, 1, −1, −1, −1, −1, −3, −3}, {−1, 3,3, −1, 3, −3, 1, −1, 3, 1, −3, −1, −3, 3, 3, −1, −1, −1, 3, −3, −3, −3,−3, −3}, {−3, −3, −1, 3, −3, −1, 1, −1, −3, 1, −1, 3, 1, 3, 1, 3, −1,−3, −1, 1, 1, −1, −3, −3}, {−3, 3, 1, 3, −1, 1, −3, 1, −3, 1, −1, −3,−1, −3, −3, −3, −3, −1, −1, −1, 1, 1, −3, −3}, {−1, −3, −1, 3, −1, 3,−3, −3, 3, 3, 1, 3, 3, −1, −3, −3, −1, 3, −3, −3, 1, 1, −3, −3}, {−1,−1, −3, −3, 3, −3, 1, 3, −3, 1, 1, −3, 3, 1, 1, −3, 3, −1, 3, 1, 3, 3,−3, −3}, {1, −3, 1, 3, −3, 3, 1, −1, −3, −3, −3, 1, −1, −3, 1, −3, −1,−1, 1, −3, −3, −3, −3, −3}, {1, 1, 1, 1, −1, 3, 1, 3, −1, −1, −3, 1, −3,1, 1, 3, −3, 1, −1, −3, 1, 3, −3, −3}, {1, 3, −3, 3, 3, −3, −3, −1, −1,3, −3, 1, −1, 3, −1, 3, 1, −1, −1, 1, −1, −1, −3, −3}, {1, 3, −1, 3, 1,1, 1, −1, 3, −3, 1, 1, −3, 3, −1, −3, 1, 1, −1, 1, 1, 3, −3, −3}, and{3, −1, −3, 1, −1, −3, 1, 3, 1, 3, −3, −3, −3, −3, 1, 3, −1, −1, −1, −3,−1, −1, −3, −3}.

The sequence in the sequence set 2C includes some or all of thefollowing sequences:

{−1, 3, −1, 3, −1, 3, 3, −1, −1, 3, −1, −1, −1, −1, 3, 3, 3, −1, −1, 3,3, 3, 3, 3}, {3, 3, −1, −1, −1, 3, 3, −1, −1, 3, 3, −1, 3, 3, −1, 3, −1,3, −1, 3, 3, 3, 3, 3}, {−3, −3, −3, −3, −3, 1, 1, −3, −3, −3, −3, −3, 1,−3, 1, 1, −3, 1, 1, −3, 1, −3, 1, −3}, {−3, 1, −3, 1, −3, 1, 1, −3, 1,1, −3, 1, −3, −3, −3, −3, −3, 1, 1, −3, −3, −3, −3, −3}, {1, 1, 1, −3,−3, 1, −3, −3, −3, 1, 1, −3, 1, 1, −3, 1, −3, −3, −3, 1, −3, 1, −3, −3},{1, −3, 1, −3, 1, −3, 3, 3, −3, 1, −1, −1, 3, −3, −3, 3, −1, −1, 3, 3,1, 1, 3, 3}, {3, 3, −3, −3, 3, 3, −1, −1, 3, 1, 1, 3, −1, −1, −3, 1, 3,3, 1, −3, 1, −3, 1, −3}, {−1, 3, −1, 3, −1, 3, −3, −3, 3, −1, 1, 1, −3,3, 3, −3, 1, 1, −3, −3, −1, −1, −3, −3}, {−3, −3, 3, 3, −3, −3, 1, 1,−3, −1, −1, −3, 1, 1, 3, −1, −3, −3, −1, 3, −1, 3, −1, 3}, {1, −3, 1,−3, 1, −1, 3, 3, −1, 3, 3, −1, −3, −3, 1, 1, 1, −3, −3, 3, 3, 3, 3, 3},{−1, 3, −1, 3, −1, 1, −3, −3, 1, −3, −3, 1, 3, 3, −1, −1, −1, 3, 3, −3,−3, −3, −3, −3}, {1, −3, −1, −3, 1, −3, 1, 1, −3, −3, −3, 1, −1, −1, 3,−1, −1, 3, 3, 3, 3, 1, 3, 3}, {−1, 3, 1, 3, −1, 3, −1, −1, 3, 3, 3, −1,1, 1, −3, 1, 1, −3, −3, −3, −3, −1, −3, −3}, {−3, 1, −3, −1, 1, −3, −1,3, 1, −3, 1, 1, −1, −3, 1, 1, 1, −1, −1, 1, 1, 3, −3, −3}, {1, −3, 3, 1,−3, 3, −1, 1, −3, 1, 1, 3, −3, 1, 1, 1, 3, 3, 1, 1, −1, −3, −3, −3}, {3,−1, 3, 1, −1, 3, 1, −3, −1, 3, −1, −1, 1, 3, −1, −1, −1, 1, 1, −1, −1,−3, 3, 3}, {−1, 3, −3, −1, 3, −3, 1, −1, 3, −1, −1, −3, 3, −1, −1, −1,−3, −3, −1, −1, 1, 3, 3, 3}, {1, 1, −3, 1, 1, 3, −1, 3, −1, 3, −1, −3,−3, 1, −3, −3, −3, −3, 1, 1, 1, 1, −3, −3}, {−1, −1, 3, 3, 3, 3, −1, −1,−1, −1, 3, −1, −1, −3, 1, −3, 1, −3, 1, 3, 3, −1, 3, 3}, {1, 1, −3, −3,−3, −3, 1, 1, 1, 1, −3, 1, 1, 3, −1, 3, −1, 3, −1, −3, −3, 1, −3, −3},{−1, −1, 3, −1, −1, −3, 1, −3, 1, −3, 1, 3, 3, −1, 3, 3, 3, 3, −1, −1,−1, −1, 3, 3}, {3, −3, 1, −3, −1, −3, −3, 3, 1, −3, 1, 1, 1, −1, 3, 1,−3, 3, 3, −3, −1, 1, 3, 3}, {−3, 3, −1, 3, 1, 3, 3, −3, −1, 3, −1, −1,−1, 1, −3, −1, 3, −3, −3, 3, 1, −1, −3, −3}, {−1, 3, 1, −3, −3, 1, 1,−1, 3, −3, 3, −1, −3, −3, 1, 3, 1, 1, 3, −3, 3, 3, 3, 3}, {1, −3, −1, 3,3, −1, −1, 1, −3, 3, −3, 1, 3, 3, −1, −3, −1, −1, −3, 3, −3, −3, −3,−3}, {1, 3, 3, −3, −3, −1, −3, 1, 3, −1, 1, −3, −3, 3, 1, −3, 1, −1, −1,−3, −1, −1, −3, −3}, {−1, −3, −3, 3, 3, 1, 3, −1, −3, 1, −1, 3, 3, −3,−1, 3, −1, 1, 1, 3, 1, 1, 3, 3}, {1, 1, −1, 3, 3, 3, 1, −3, 3, −1, −3,−3, 1, 1, 3, −1, 1, −3, −1, −1, −1, 3, −3, −3}, {−1, −1, 1, −3, −3, −3,−1, 3, −3, 1, 3, 3, −1, −1, −3, 1, −1, 3, 1, 1, 1, −3, 3, 3}, {1, −3,−1, 3, −3, 1, −1, 3, −1, 3, 3, 3, 1, −3, 1, 1, 1, 1, −1, −1, 1, 1, 3,3}, {−1, 3, 1, −3, 3, −1, 1, −3, 1, −3, −3, −3, −1, 3, −1, −1, −1, −1,1, 1, −1, −1, −3, −3}, {3, −3, 3, −1, 1, −1, 3, −3, 3, 3, 1, 3, 3, 3, 3,−1, −3, 1, 1, −3, −1, 1, −3, −3}, {−3, 3, −3, 1, −1, 1, −3, 3, −3, −3,−1, −3, −3, −3, −3, 1, 3, −1, −1, 3, 1, −1, 3, 3}, {1, −3, −1, 3, 3, −1,3, −3, −3, −1, −3, 1, −1, 3, 3, −1, −3, 1, 3, −3, −3, −3, 3, 3}, {−1, 3,1, −3, −3, 1, −3, 3, 3, 1, 3, −1, 1, −3, −3, 1, 3, −1, −3, 3, 3, 3, −3,−3}, {−1, −3, 3, 1, −3, −3, 1, 1, 3, −1, −1, 1, −3, 3, 3, −3, 1, −3, 1,3, 3, 3, 3, 3}, {1, 3, −3, −1, 1, −3, 3, 1, −1, 3, −3, −3, 3, −1, 1, −1,3, −3, 3, −3, 3, 3, 3, 3}, {−1, −3, 3, 1, −1, 3, −3, −1, 1, −3, 3, 3,−3, 1, −1, 1, −3, 3, −3, 3, −3, −3, −3, −3}, {1, 3, −3, −1, 3, 3, −1,−1, −3, 1, 1, −1, 3, −3, −3, 3, −1, 3, −1, −3, −3, −3, −3, −3}, {−1, 3,−1, 3, −1, 3, −1, −1, 3, −1, −1, 3, −1, −1, 3, 3, 3, −1, −1, 3, 3, 3, 3,3}, {1, 3, −3, −3, −1, 3, 3, −1, 1, −1, −1, 1, −3, 3, 3, −3, 3, −3, 3,3, 1, −3, 3, 3}, {−1, −3, 3, 3, 1, −3, −3, 1, −1, 1, 1, −1, 3, −3, −3,3, −3, 3, −3, −3, −1, 3, −3, −3}, {−1, 1, −3, 3, −1, 1, −3, −3, 1, 1, 3,−1, −3, −3, −1, 3, 3, 1, 3, 1, 1, 3, 3, 3}, {1, −1, 3, −3, 1, −1, 3, 3,−1, −1, −3, 1, 3, 3, 1, −3, −3, −1, −3, −1, −1, −3, −3, −3}, {3, 1, −1,−3, 1, 3, −3, 1, 3, 3, 1, 1, 1, −1, 1, −1, 3, −1, 1, 1, 3, 3, −3, −3},{−3, −1, 1, 3, −1, −3, 3, −1, −3, −3, −1, −1, −1, 1, −1, 1, −3, 1, −1,−1, −3, −3, 3, 3}, {−3, −3, 3, 3, −3, −1, −3, −3, 3, −3, −1, 1, 3, 1, 3,1, 3, −1, −1, −3, 1, −1, 3, 3}, {3, 3, −3, −3, 3, 1, 3, 3, −3, 3, 1, −1,−3, −1, −3, −1, −3, 1, 1, 3, −1, 1, −3, −3}, {−3, −3, 1, −1, 3, 1, 1,−3, −1, −3, −1, −3, −1, 1, 3, −3, 3, 3, 1, 3, −3, −3, 3, 3}, {3, 3, −1,1, −3, −1, −1, 3, 1, 3, 1, 3, 1, −1, −3, 3, −3, −3, −1, −3, 3, 3, −3,−3}, {−1, −3, 3, −1, −3, 1, 1, −3, 1, 3, 1, −3, −3, −3, −3, −1, 3, 3, 3,1, −3, −1, 3, 3}, {1, 3, −3, 1, 3, −1, −1, 3, −1, −3, −1, 3, 3, 3, 3, 1,−3, −3, −3, −1, 3, 1, −3, −3}, {3, −3, 3, −1, −3, −3, −1, 1, −1, 3, −3,−1, 1, −1, −1, 3, 1, −1, 1, −1, −1, −3, −3, −3}, {−3, 3, −3, 1, 3, 3, 1,−1, 1, −3, 3, 1, −1, 1, 1, −3, −1, 1, −1, 1, 1, 3, 3, 3}, {−1, −3, −3,−3, 3, 3, −3, 1, 1, −3, 3, −1, 1, −3, 3, −1, 3, −1, 1, 3, 3, 3, −3, −3},{−1, −3, 1, −1, −3, 1, −3, −1, 1, 3, 3, −3, 1, 3, 3, −3, 3, −3, 1, −1,−1, −3, 3, 3}, {1, 3, −1, 1, 3, −1, 3, 1, −1, −3, −3, 3, −1, −3, −3, 3,−3, 3, −1, 1, 1, 3, −3, −3}, {1, 3, 3, 3, −3, −3, 3, −1, −1, 3, −3, 1,−1, 3, −3, 1, −3, 1, −1, −3, −3, −3, 3, 3}, {−3, 1, 3, −3, −1, 3, 3, −1,−3, 3, 1, −3, 1, 1, 1, −1, −3, −1, 3, 1, 3, −3, −3, −3}, {3, −1, −3, 3,1, −3, −3, 1, 3, −3, −1, 3, −1, −1, −1, 1, 3, 1, −3, −1, −3, 3, 3, 3},{−1, 3, −1, −3, 3, −3, −3, 3, −3, −1, 3, −1, −1, −1, 1, 3, −3, −3, 1, 1,−1, −3, 3, 3}, {1, −3, 1, 3, −3, 3, 3, −3, 3, 1, −3, 1, 1, 1, −1, −3, 3,3, −1, −1, 1, 3, −3, −3}, {−3, 1, −3, 1, −1, 1, 1, −3, −3, −3, −3, 3, 1,3, −3, −3, 3, 3, −1, −3, −3, 1, −3, −3}, {3, −1, 3, −1, 1, −1, −1, 3, 3,3, 3, −3, −1, −3, 3, 3, −3, −3, 1, 3, 3, −1, 3, 3}, {3, 3, 3, 3, 3, 3,−3, −3, 1, 1, 1, −1, −3, 3, −1, 3, 3, −1, 1, −3, 1, −3, 1, −3}, {−1, −1,−1, −1, −1, −1, −3, −3, 1, 1, 1, 3, −3, −1, 3, −1, −1, 3, 1, −3, 1, −3,1, −3}, {1, −1, 1, −1, 1, −3, 1, −3, 3, 1, −1, −3, −3, 3, 3, −1, 3, −3,−1, 1, 3, 3, −3, −3}, {1, 3, −1, 1, −3, 1, −3, 1, −1, −3, −1, −1, 1, 1,1, 1, 1, −1, −3, 3, −1, −1, 3, 3}, {−1, −3, 1, −1, 3, −1, 3, −1, 1, 3,1, 1, −1, −1, −1, −1, −1, 1, 3, −3, 1, 1, −3, −3}, {−1, 1, −1, 1, −1, 3,−1, 3, −3, −1, 1, 3, 3, −3, −3, 1, −3, 3, 1, −1, −3, −3, 3, 3}, {3, 1,1, −1, −1, 3, −3, 1, −1, 3, 1, −1, −1, 1, −1, 3, −3, −1, −1, 1, 3, 1, 3,3}, {−3, −1, 3, 3, −1, 3, −3, 1, −3, 3, 3, −1, 1, 1, 1, −1, −1, −3, 1,−1, 1, 1, 3, 3}, {−3, −1, −1, 1, 1, −3, 3, −1, 1, −3, −1, 1, 1, −1, 1,−3, 3, 1, 1, −1, −3, −1, −3, −3}, {3, 1, −3, −3, 1, −3, 3, −1, 3, −3,−3, 1, −1, −1, −1, 1, 1, 3, −1, 1, −1, −1, −3, −3}, {1, −1, 3, 1, −3,−1, 3, 1, −1, −1, 3, −3, 3, −1, 1, 3, 1, 3, −3, −1, −3, −3, −3, −3},{−1, 1, −3, −1, 3, 1, −3, −1, 1, 1, −3, 3, −3, 1, −1, −3, −1, −3, 3, 1,3, 3, 3, 3}, {1, 3, −3, −1, −1, 3, −1, 3, 3, −1, 3, 1, 1, −3, 3, −3, −3,−3, 3, −1, −3, −3, 3, 3}, {−1, −3, 3, 1, 1, −3, 1, −3, −3, 1, −3, −1,−1, 3, −3, 3, 3, 3, −3, 1, 3, 3, −3, −3}, {3, −1, −1, 1, −1, −1, −3, 1,1, 3, 1, 1, −1, 3, 1, 3, −1, −1, −3, 1, −1, 1, −3, −3}, {−3, 1, 1, −1,1, 1, 3, −1, −1, −3, −1, −1, 1, −3, −1, −3, 1, 1, 3, −1, 1, −1, 3, 3},{3, 3, 3, 3, 3, 3, −1, −1, 3, 3, 3, 3, −1, −1, 3, −1, −1, 3, −1, 3, −1,3, −1, 3}, {−1, 3, −1, 3, −1, −1, 3, −1, −1, 3, 3, −1, −1, −1, −1, 3,−1, −1, −1, 3, 3, 3, 3, 3}, {1, −1, 3, 1, 3, 1, −3, 3, 3, −1, −3, −1,−1, −1, 3, −3, −3, −3, 1, 3, −1, 1, −3, −3}, {−1, 1, −3, −1, −3, −1, 3,−3, −3, 1, 3, 1, 1, 1, −3, 3, 3, 3, −1, −3, 1, −1, 3, 3}, {−1, 1, −3,−1, 3, −3, −1, −3, 3, 3, −1, −3, 1, 3, 3, 1, −1, 1, −1, 3, 1, 3, 3, 3},{1, −1, 3, 1, −3, 3, 1, 3, −3, −3, 1, 3, −1, −3, −3, −1, 1, −1, 1, −3,−1, −3, −3, −3}, {1, 3, −3, −3, 1, −1, 3, 3, −1, 3, −3, −3, 3, −1, −3,−1, 3, −1, −1, −1, −3, −3, 3, 3}, {−1, −3, 3, 3, −1, 1, −3, −3, 1, −3,3, 3, −3, 1, 3, 1, −3, 1, 1, 1, 3, 3, −3, −3}, {3, −3, −1, 1, −1, −1, 3,1, 3, 3, −1, −3, 1, −3, 1, −3, 1, −1, −1, −3, −1, −1, −3, −3}, {−3, 3,1, −1, 1, 1, −3, −1, −3, −3, 1, 3, −1, 3, −1, 3, −1, 1, 1, 3, 1, 1, 3,3}, {−3, 1, 3, −1, 3, 1, 3, −1, −1, −3, −3, 1, −3, 3, 1, −3, 3, 3, 3, 1,3, 3, −3, −3}, {3, −1, −3, 1, −3, −1, −3, 1, 1, 3, 3, −1, 3, −3, −1, 3,−3, −3, −3, −1, −3, −3, 3, 3}, {−1, 3, −3, 1, 3, 1, −3, 1, −1, −1, −3,3, 3, 3, −1, −3, 1, 1, 3, 1, 1, 1, 3, 3}, {1, −3, 3, −1, −3, −1, 3, −1,1, 1, 3, −3, −3, −3, 1, 3, −1, −1, −3, −1, −1, −1, −3, −3}, {−3, 1, 3,−1, 1, −3, −1, −3, 1, −1, 3, 1, −1, −1, −3, −1, −1, −1, −3, −1, −1, 1,3, 3}, {−1, 3, −3, −1, 3, −3, 3, −1, 3, −3, 3, −1, −3, 3, 3, 1, 1, −1,1, 1, 3, 3, −3, −3}, {3, −1, −3, 1, −1, 3, 1, 3, −1, 1, −3, −1, 1, 1, 3,1, 1, 1, 3, 1, 1, −1, −3, −3}, {1, −3, 3, 1, −3, 3, −3, 1, −3, 3, −3, 1,3, −3, −3, −1, −1, 1, −1, −1, −3, −3, 3, 3}, {3, −1, −1, 3, 1, −3, −3,−1, −1, 3, −3, 1, −1, −3, −3, 3, 1, 3, −1, 3, −3, −3, −3, −3}, {3, −1,3, −1, 1, 1, 1, 3, 1, −1, 3, 1, −1, −1, 1, 1, −3, −1, 3, 3, 1, 1, −3,−3}, {−1, 3, 3, −1, 1, −3, −3, 3, 3, −1, −3, 1, 3, −3, −3, −1, 1, −1, 3,−1, −3, −3, −3, −3}, {−3, 1, −3, 1, −1, −1, −1, −3, −1, 1, −3, −1, 1, 1,−1, −1, 3, 1, −3, −3, −1, −1, 3, 3}, {3, −3, −1, 1, −3, −1, 3, −1, 3,−1, −3, −1, −1, 1, 1, 1, −1, −3, 1, −1, −3, −3, −3, −3}, {−3, 3, 1, −1,3, 1, −3, 1, −3, 1, 3, 1, 1, −1, −1, −1, 1, 3, −1, 1, 3, 3, 3, 3}, {1,3, −3, −1, 3, −1, −3, 1, −3, −1, 1, 1, 3, 3, −1, −3, 3, 1, −1, −1, −3,−3, −3, −3}, {−1, −3, 3, 1, −3, 1, 3, −1, 3, 1, −1, −1, −3, −3, 1, 3,−3, −1, 1, 1, 3, 3, 3, 3}, {−1, 3, −1, 3, −3, 1, 3, −1, 1, 1, −3, 3, 3,−3, −3, 1, −1, 3, 3, 3, 1, 1, 3, 3}, {1, −3, 1, −3, 3, −1, −3, 1, −1,−1, 3, −3, −3, 3, 3, −1, 1, −3, −3, −3, −1, −1, −3, −3}, {3, −1, 3, −1,3, −1, −3, 3, 1, 3, −1, −1, −3, −1, 1, 3, 3, −3, −3, 3, 3, −3, 3, 3},{−3, 1, −3, 1, −3, 1, 3, −3, −1, −3, 1, 1, 3, 1, −1, −3, −3, 3, 3, −3,−3, 3, −3, −3}, {3, 3, −3, 3, 3, −3, −3, 3, 3, 1, −1, −3, −1, −1, 3, 1,3, −3, −1, 3, −1, 3, −1, 3}, {−3, −3, 3, −3, −3, 3, 3, −3, −3, −1, 1, 3,1, 1, −3, −1, −3, 3, 1, −3, 1, −3, 1, −3}, {3, 1, −3, −1, −1, 3, 1, 3,−1, 1, −3, 3, −1, 3, 3, 1, −1, −3, −3, −1, −3, −3, −3, −3}, {−3, −1, 3,1, 1, −3, −1, −3, 1, −1, 3, −3, 1, −3, −3, −1, 1, 3, 3, 1, 3, 3, 3, 3},{−3, −3, −1, 3, −3, 3, 3, −1, −1, 1, −3, −1, −1, −3, 1, −1, −1, 3, 3,−3, 3, −1, −3, −3}, {3, 3, 1, −3, 3, −3, −3, 1, 1, −1, 3, 1, 1, 3, −1,1, 1, −3, −3, 3, −3, 1, 3, 3}, {1, 3, −1, −1, 1, −1, 3, 1, −1, 1, 1, −3,1, 3, 1, 3, −1, −3, −3, −1, −1, −3, 3, 3}, {1, −1, 3, −1, −3, −3, 3, −1,1, 1, −3, −3, −1, 1, −1, −1, 3, −1, 1, −3, −3, 3, −3, −3}, {−1, 1, −3,1, 3, 3, −3, 1, −1, −1, 3, 3, 1, −1, 1, 1, −3, 1, −1, 3, 3, −3, 3, 3},{−1, −3, 1, 1, −1, 1, −3, −1, 1, −1, −1, 3, −1, −3, −1, −3, 1, 3, 3, 1,1, 3, −3, −3}, {3, 1, −3, 3, −3, 3, 1, −1, −1, 1, 1, 1, −3, −3, 1, 3, 3,3, −1, 3, −3, 1, 3, 3}, {−3, −1, 3, −3, 3, −3, −1, 1, 1, −1, −1, −1, 3,3, −1, −3, −3, −3, 1, −3, 3, −1, −3, −3}, {3, −3, −3, −3, 1, 1, −1, −1,1, 3, −3, −1, 3, −1, 3, −1, −3, −3, −1, −3, 3, −1, −3, −3}, {−1, −3, −3,−3, 1, 3, 3, 1, −1, −3, 3, −1, 3, −1, 3, −3, −3, 3, −3, −1, 3, −3, −3},{3, 3, 3, −3, −3, 3, −1, 1, −3, 1, −3, 1, −1, −3, −1, −3, 3, 1, 3, −3,−1, 1, −3, −3}, {1, 1, −3, −1, 1, 3, −3, 3, 1, −1, 1, −1, −3, 1, −3, 1,−3, −1, 3, 1, 1, 3, 3, 3}, {−1, −1, −1, −3, −3, −1, 3, 1, −3, 1, −3, 1,3, −3, 3, −3, −1, 1, −1, −3, 1, 1, −3, −3}, {−1, −1, 3, 1, −1, −3, 3,−3, −1, 1, −1, 1, 3, −1, 3, −1, 3, 1, −3, −1, −1, −3, −3, −3}, {3, −1,3, 3, 3, 3, −1, 3, −1, 3, 3, 3, −1, 3, 3, −1, −1, 3, −1, −1, −1, −1, 3,3}, {1, −3, −3, 1, −3, 1, 1, 1, −3, −3, 1, 1, 1, −3, 1, 1, 1, 1, 1, −3,1, −3, −3, −3}, {−3, 1, −3, 3, 1, −3, 1, −1, −1, −3, −3, −1, 3, −3, 1,−1, −3, −3, 1, 1, 1, 3, 3, 3}, {−1, 3, −1, 1, −3, 1, 1, −3, 3, 1, 1, 3,3, −3, 1, −1, 3, 1, 1, 1, −1, −3, −3, −3}, {3, −1, 3, −3, −1, 3, −1, 1,1, 3, 3, 1, −3, 3, −1, 1, 3, 3, −1, −1, −1, −3, −3, −3}, {1, −3, 1, −1,3, −1, −1, 3, −3, −1, −1, −3, −3, 3, −1, 1, −3, −1, −1, −1, 1, 3, 3, 3},{3, −1, 1, −1, −3, −1, −3, −1, −3, −3, 1, −3, 3, −1, −1, 3, −3, 1, 1, 1,3, 3, −3, −3}, {−3, 1, −1, 1, 3, 1, 3, 1, 3, 3, −1, 3, −3, 1, 1, −3, 3,−1, −1, −1, −3, −3, 3, 3}, {3, −1, 1, −3, −1, 3, −1, −1, −1, 3, −3, −3,−3, 3, −1, −1, −1, 3, −1, −3, 1, −1, 3, 3}, {−3, 1, −1, 3, 1, −3, 1, 1,1, −3, 3, 3, 3, −3, 1, 1, 1, −3, 1, 3, −1, 1, −3, −3}, {−3, 3, −1, −1,1, −1, −3, 1, 1, 3, −1, 3, −1, 1, 3, −3, 1, −1, −1, −1, 1, −1, −3, −3},{3, −3, 1, 1, −1, 1, 3, −1, −1, −3, 1, −3, 1, −1, −3, 3, −1, 1, 1, 1,−1, 1, 3, 3}, {3, −1, 3, −3, 1, −3, 3, 1, −3, −3, −1, 3, 3, 3, 3, −1,−1, 1, 1, 1, −1, 3, 3, 3}, {3, −1, 3, 1, −3, 1, 3, −3, 1, 1, −1, 3, 3,3, 3, −1, −1, −3, −3, −3, −1, 3, 3, 3}, {−3, −3, 1, 1, −3, −3, −3, −3,3, 3, −3, 3, 3, −3, −3, −1, 1, −1, −1, 3, −1, 3, −1, 3}, {3, 3, −1, −1,3, 3, 3, 3, −3, −3, 3, −3, −3, 3, 3, 1, −1, 1, 1, −3, 1, −3, 1, −3},{−3, −1, 1, 1, 1, −3, 1, 3, 3, −3, 3, −1, 1, −3, 1, −1, −3, −1, −1, 3,−1, −1, −3, −3}, {3, 1, −1, −1, −1, 3, −1, −3, −3, 3, −3, 1, −1, 3, −1,1, 3, 1, 1, −3, 1, 1, 3, 3}, {−1, −3, 1, −3, 1, −1, 3, 1, 3, −3, 1, −3,−3, −3, −1, 3, 3, 3, 3, 3, −1, −1, 3, 3}, {1, 3, −1, 3, −1, 1, −3, −1,−3, 3, −1, 3, 3, 3, 1, −3, −3, −3, −3, −3, 1, 1, −3, −3}, {1, 3, 3, −1,1, 1, 3, 1, −3, 3, −1, −1, −1, −3, −3, 3, 1, 3, −1, 3, −3, 1, −3, −3},{−1, −3, −3, 1, −1, −1, −3, −1, 3, −3, 1, 1, 1, 3, 3, −3, −1, −3, 1, −3,3, −1, 3, 3}, {−3, 3, 1, −1, 3, 1, −3, −1, −3, 1, −3, −1, 1, 3, −1, 1,−3, −3, −3, −1, −1, −1, −3, −3}, {3, −3, −1, 1, −3, −1, 3, 1, 3, −1, 3,1, −1, −3, 1, −1, 3, 3, 3, 1, 1, 1, 3, 3}, {3, −1, −3, 1, 3, 1, 1, −3,−3, −1, 1, 1, −3, 1, 3, −1, 3, 3, −1, −3, −3, −3, −3, −3}, {3, −1, 3,−1, 3, 1, 1, −3, −3, −3, −1, −1, −1, 3, −3, −1, 3, 3, −1, −3, −1, −1,−3, −3}, {−3, 1, −3, 1, −3, −1, −1, 3, 3, 3, 1, 1, 1, −3, 3, 1, −3, −3,1, 3, 1, 1, 3, 3}, {−1, 3, −3, 1, −1, 1, 1, −3, −3, 3, 1, 1, −3, 1, −1,3, −1, −1, 3, −3, −3, −3, −3, −3}, {1, −3, −3, 1, 1, 1, −3, 3, 1, −1, 3,−1, 1, −3, 1, −1, 1, −1, −1, −1, 3, 3, 3, 3}, {−1, 3, 3, −1, −1, −1, 3,−3, −1, 1, −3, 1, −1, 3, −1, 1, −1, 1, 1, 1, −3, −3, −3, −3}, {−3, 1, 1,−3, −3, 1, 1, −3, −3, 3, −1, 3, −1, −3, −3, −3, −1, 1, −1, 1, −3, −3,−3, −3}, {3, −1, −1, 3, 3, −1, −1, 3, 3, −3, 1, −3, 1, 3, 3, 3, 1, −1,1, −1, 3, 3, 3, 3}, {3, 1, −3, −1, 1, −1, 3, −3, 1, −1, 3, −1, −3, 3,−3, 1, 1, −3, −3, 3, −3, −3, −3, −3}, {−3, −1, 3, 1, −1, 1, −3, 3, −1,1, −3, 1, 3, −3, 3, −1, −1, 3, 3, −3, 3, 3, 3, 3}, {−3, 3, 1, 1, −1, −1,3, −1, 1, −3, 1, −1, −1, 3, −1, −1, 1, −3, −1, −1, 1, 1, 3, 3}, {3, −3,−1, −1, 1, 1, −3, 1, −1, 3, −1, 1, 1, −3, 1, 1, −1, 3, 1, 1, −1, −1, −3,−3}, {−3, 3, 1, −1, 3, 1, −1, 1, 3, 3, 3, 1, 3, 1, 3, −1, −3, −1, 1, 3,−1, 3, −3, −3}, {3, 1, −3, −1, 1, −3, 1, −3, −3, −1, 3, 3, −1, −1, −3,3, −1, 3, 3, 3, −3, −3, −3, −3}, {−3, −1, 3, 1, −1, 3, −1, 3, 3, 1, −3,−3, 1, 1, 3, −3, 1, −3, −3, −3, 3, 3, 3, 3}, {3, −3, −1, 1, −3, −1, 1,−1, −3, −3, −3, −1, −3, −1, −3, 1, 3, 1, −1, −3, 1, −3, 3, 3}, {−3, 3,−1, 1, −1, 3, 1, 3, 3, −3, 3, 1, 1, 1, 1, −3, 1, 1, −1, 3, −3, −1, 3,3}, {3, −3, 1, −1, 1, −3, −1, −3, −3, 3, −3, −1, −1, −1, −1, 3, −1, −1,1, −3, 3, 1, −3, −3}, and {−3, 1, 1, −3, −3, 1, 1, −3, 1, −3, 1, 1, −3,−3, −3, −3, 1, −3, 1, −3, −3, −3, −3, −3}.

The sequence in the third sequence set includes at least one of thefollowing: a sequence in a sequence set 3A, a sequence in a sequence set3B, and a sequence in a sequence set 3C. The sequence in the sequenceset 3A includes some or all of the following sequences:

{−1, 1, 1, −3, −3, 3}, {−1, −3, −3, 1, 1, 3}, {−1, −3, 1, 3, 3, 1}, {1,3, −1, −3, −3, −1}, {−1, −3, −1, 1, −1, 1}, {−1, 1, −1, 1, 3, 1}, {3, 3,−1, −1, −1, −1}, {−3, −3, −3, −3, 1, 1}, {−3, 1, 1, −3, −3, 1}, {−3, −3,−3, 1, 1, 1}, {−3, 1, −1, −3, 3, 3}, and {−3, −1, −1, −1, −1, −3}.

The sequence in the sequence set 3B includes some or all of thefollowing sequences:

{1, 1, −3, 3, 1, 3}, {1, 1, −1, −3, 1, −3}, {1, 1, 1, −1, −3, 1}, {1, 1,1, 3, −3, 1}, {1, 1, 3, −3, 1, −3}, {1, 1, −3, −1, −3, −1}, {1, 1, −1,1, 1, −3}, {1, 1, 3, 3, −1, 3}, {1, 1, 1, −3, 3, −1}, {1, 1, −1, −1, 3,−1}, {1, 1, 1, −3, −1, 3}, {1, 1, 1, −3, 1, −1}, {1, 1, 1, −3, 1, 3},{1, 1, −1, −3, −1, 1}, {1, 1, 3, −3, 3, 1}, {1, 1, −3, −3, 1, −3}, {1,1, −3, 1, 3, 3}, {1, 1, 3, −1, 3, 3}, {1, 1, −1, 3, −1, −1}, {1, 1, −3,1, −1, −1}, {1, 1, 3, −1, −3, 3}, {1, 1, 1, −1, 3, −3}, {1, 1, −1, 3,−3, −1}, {1, 1, 1, 3, −1, −3}, {1, 1, 3, −1, 1, −1}, {1, 1, −3, 3, −1,1}, {1, 1, −3, −1, 3, 1}, {1, 1, −1, 3, 1, 3}, and {1, 1, −3, 1, 1, 1}.

The sequence in the sequence set 3C includes some or all of thefollowing sequences: {1, 1, −1, −1, −3, 1}, {1, 1, −1, −1, 1, −3}, {1,1, −1, −3, −3, −1}, {1, 1, −1, 3, −1, −3}, {1, 1, −1, 3, −1, 3}, {1, 1,−1, 3, −3, 1}, {1, 1, −1, 3, 1, −3}, {1, 1, −1, 1, −3, 1}, {1, 1, −1, 1,3, −3}, {1, 1, −1, 1, 3, 1}, {1, 1, −3, −1, −1, −1}, {1, 1, −3, −1, 3,−1}, {1, 1, −3, 3, −1, 3}, {1, 1, −3, 3, 3, 3}, {1, 1, −3, 1, 1, −1},{1, 1, −3, 1, 1, 3}, {1, 1, 3, −1, −3, 1}, {1, 1, 3, −1, 3, −1}, {1, 1,3, −1, 3, −3}, {1, 1, 3, −1, 1, −3}, {1, 1, 3, −3, −3, 3}, {1, 1, 3, 3,−3, 1}, {1, 1, 3, 3, 1, −3}, {1, 1, 3, 1, −1, −3}, {1, 1, 3, 1, −1, 1},{1, 1, 3, 1, −3, 1}, {1, 1, 1, −1, −1, 3}, {1, 1, 1, −1, 3, 3}, {1, 1,1, −1, 1, −3}, {1, 1, 1, 3, −1, −1}, {1, 1, 1, 3, 3, −1}, {1, 1, 1, 3,1, −3}, {1, 1, 1, 1, −1, 3}, {1, 1, 1, 1, −3, −1}, {1, 1, 1, 1, −3, 3},and {1, 1, 1, 1, 3, −1}.

A PAPR of a sequence {f_(n)} corresponding to the sequence in the set 3Ais less than 4.2597 dB, and a cubic metric (CM) value of the sequence{f_(n)} is less than 1.5140 dB. A PAPR of a sequence {f_(n)}corresponding to the sequence in the set 3B is less than 4.7 dB, and acubic metric (CM) value of the sequence {f_(n)} is less than 2.4 dB.

An equivalent sequence of a sequence {s_(n)} in each sequence setdescribed above may be represented by {q_(n)}. An element q_(n) in theequivalent sequence {q_(n)} meets q_(n)=s_(n)+u_(n)(mod 8). Duringspecific implementation, optionally, a sequence {u_(n)} including u_(n)includes:u _(n) =f+g·n(mod 8), where n=0,1, . . . , or N−1, N is a sequencelength, f∈{0,2,4,6}, and g∈{0,2,4,6}.

For example, when N is 24, {u_(n)} is the following 16 sequences:

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0}, {0, 2, 4, 6, 0, 2, 4, 6, 0, 2, 4, 6, 0, 2, 4, 6, 0, 2, 4, 6, 0, 2,4, 6}, {0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0,4, 0, 4}, {0, 6, 4, 2, 0, 6, 4, 2, 0, 6, 4, 2, 0, 6, 4, 2, 0, 6, 4, 2,0, 6, 4, 2}, {2, 0, 6, 4, 2, 0, 6, 4, 2, 0, 6, 4, 2, 0, 6, 4, 2, 0, 6,4, 2, 0, 6, 4}, {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,2, 2, 2, 2, 2, 2}, {2, 4, 6, 0, 2, 4, 6, 0, 2, 4, 6, 0, 2, 4, 6, 0, 2,4, 6, 0, 2, 4, 6, 0}, {2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6,2, 6, 2, 6, 2, 6, 2, 6}, {4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4,0, 4, 0, 4, 0, 4, 0, 4, 0}, {4, 2, 0, 6, 4, 2, 0, 6, 4, 2, 0, 6, 4, 2,0, 6, 4, 2, 0, 6, 4, 2, 0, 6}, {4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4}, {4, 6, 0, 2, 4, 6, 0, 2, 4, 6, 0, 2,4, 6, 0, 2, 4, 6, 0, 2, 4, 6, 0, 2}, {6, 0, 2, 4, 6, 0, 2, 4, 6, 0, 2,4, 6, 0, 2, 4, 6, 0, 2, 4, 6, 0, 2, 4}, {6, 2, 6, 2, 6, 2, 6, 2, 6, 2,6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2}, {6, 4, 2, 0, 6, 4, 2, 0, 6,4, 2, 0, 6, 4, 2, 0, 6, 4, 2, 0, 6, 4, 2, 0}, and {6, 6, 6, 6, 6, 6, 6,6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6}.

For example, a sequence {−3, 3, 1, −1, 1, −1, −3, −1, 3, −3, −3, −1, 1,3, −3, 3, 3, −1, 3, −3, 3, −3, −3, −3} is equivalent to the following 16sequences:

{1, 1, 1, 1, −3, −3, −3, 1, −1, 3, −3, 1, −3, 1, −3, −3, −1, −3, 3, −1,−1, 3, −3, −1}, {1, 3, −3, −1, −3, −1, 1, −1, −1, −3, 1, −1, −3, 3, 1,3, −1, −1, −1, −3, −1, −3, 1, −3}, {1, −3, 1, −3, −3, 1, −3, −3, −1, −1,−3, −3, −3, −3, −3, 1, −1, 1, 3, 3, −1, −1, −3, 3}, {1, −1, −3, 3, −3,3, 1, 3, −1, 1, 1, 3, −3, −1, 1, −1, −1, 3, −1, 1, −1, 1, 1, 1}, {3, 1,−1, −3, −1, −3, 3, −3, 1, 3, 3, −3, −1, 1, 3, 1, 1, −3, 1, 3, 1, 3, 3,3}, {3, 3, 3, 3, −1, −1, −1, 3, 1, −3, −1, 3, −1, 3, −1, −1, 1, −1, −3,1, 1, −3, −1, 1}, {3, −3, −1, 1, −1, 1, 3, 1, 1, −1, 3, 1, −1, −3, 3,−3, 1, 1, 1, −1, 1, −1, 3, −1}, {3, −1, 3, −1, −1, 3, −1, −1, 1, 1, −1,−1, −1, −1, −1, 3, 1, 3, −3, −3, 1, 1, −1, −3}, {−3, 1, −3, 1, 1, −3, 1,1, 3, 3, 1, 1, 1, 1, 1, −3, 3, −3, −1, −1, 3, 3, 1, −1}, {−3, 3, 1, −1,1, −1, −3, −1, 3, −3, −3, −1, 1, 3, −3, 3, 3, −1, 3, −3, 3, −3, −3, −3},{−3, −3, −3, −3, 1, 1, 1, −3, 3, −1, 1, −3, 1, −3, 1, 1, 3, 1, −1, 3, 3,−1, 1, 3}, {−3, −1, 1, 3, 1, 3, −3, 3, 3, 1, −3, 3, 1, −1, −3, −1, 3, 3,3, 1, 3, 1, −3, 1}, {−1, 1, 3, −3, 3, −3, −1, −3, −3, 3, −1, −3, 3, 1,−1, 1, −3, −3, −3, 3, −3, 3, −1, 3}, {−1, 3, −1, 3, 3, −1, 3, 3, −3, −3,3, 3, 3, 3, 3, −1, −3, −1, 1, 1, −3, −3, 3, 1}, {−1, −3, 3, 1, 3, 1, −1,1, −3, −1, −1, 1, 3, −3, −1, −3, −3, 1, −3, −1, −3, −1, −1, −1}, and{−1, −1, −1, −1, 3, 3, 3, −1, −3, 1, 3, −1, 3, −1, 3, 3, −3, 3, 1, −3,−3, 1, 3, −3}.

Herein, in the case that an equivalent sequence of {s_(n)} is adifference between a sequence {u·e^(πjs) ^(n) ^(/4)} and a sequence{u·e^(πjq) ^(n) ^(/4)} is a constant, or a constant and a cyclic shifttransformation. Therefore, a maximum value of an absolute value of acyclic shift autocorrelation between the two sequences is 1.

In a possible example, a process of determining the sequence {f_(n)}consisting the N elements by the terminal after the terminal accessesthe network may be shown in FIG. 2. A specific procedure is as follows:

The terminal determines the sequence {x_(n)} and A. The value of nranges from 0 to N−1, and A is a non-zero complex number. The sequence{x_(n)} may be stored by the terminal, or may be configured by thenetwork device for the terminal, or may be calculated by the terminalbased on a predefined formula. For example, the sequence {x_(n)} isobtained by using a disclosed element x_(n)=u·exp(π·j·s_(n)/4) in{x_(n)}, and a sequence {f_(n)=A·x_(n)} is obtained by separatelymultiplying A by x_(n). A value range of A is {1, −1, j, −j}.

S102. The terminal maps the sequence {f_(n)} consisting the N elementsto N subcarriers to generate a first signal, and sends the first signalto a network device.

Herein, S102 is mainly performed by the terminal by respectively mappingthe N elements in the configured sequence {f_(n)} to the N subcarriersto generate the first signal, and sending the first signal to thenetwork device.

Optionally, a specific process of mapping, by the terminal, the sequence{f_(n)} consisting the N elements to the N subcarriers to generate thefirst signal, and sending the first signal to the network device isshown in FIG. 3, and includes the following steps.

S301. The terminal maps the sequence {f_(n)} consisting the N elementsto the N subcarriers to obtain an N-element frequency domain signal(namely, a frequency domain signal consisting of N elements).

In FIG. 4a and FIG. 4b disclosed in the embodiments of this application,s indicates a subcarrier index that is in a communications system andthat is of a first subcarrier in the N subcarriers to which the sequence{f_(n)} is mapped.

Optionally, the terminal maps the sequence {f_(n)} consisting the Nelements to N consecutive subcarriers. As shown in FIG. 4a , optionally,elements f₀ to f_(N-1) in the sequence {f_(n)} are respectively mappedto N consecutive subcarriers, and the subcarriers are numbered s+0, s+1,. . . , and s+N−1.

In a possible example, the terminal successively maps the N elements inthe sequence {f_(n)} to the N subcarriers in descending order. Oneelement in the sequence {f_(n)} is mapped to one frequency domainsubcarrier. The frequency domain subcarrier is a smallest unit offrequency domain resources, and is used to carry data information.

In a possible example, the terminal successively maps the N elements inthe sequence {f_(n)} to the N subcarriers in ascending order. Mappingone element in the sequence {f_(n)} to one subcarrier means that theelement is carried on the subcarrier. After the mapping, sending data bythe terminal in a radio frequency manner is equivalent to sending theelement on the subcarrier. In the communications system, differentterminals may send data by using different subcarriers. Locations of theN subcarriers in a plurality of subcarriers in the communications systemmay be predefined or configured by the network device by usingsignaling.

Optionally, the N elements in the sequence {f_(n)} may be respectivelymapped to N equally spaced subcarriers. As shown in FIG. 4b ,optionally, spacings between the N subcarriers are 1, and the Nsubcarriers are equally spaced in frequency domain. Spacings betweensubcarriers to which elements f₀ to f_(N-1) in the sequence {f_(n)} aremapped are one subcarrier. Specifically, the elements f₀ to f_(N-1) inthe sequence {f_(n)} are respectively mapped to N equally spacedsubcarriers, and the subcarriers are numbered s+0, s+2, . . . , ands+2(N−1).

In this embodiment of this application, a manner of respectively mappingthe N elements in the sequence {f_(n)} to the N subcarriers is notlimited to the foregoing manner.

S302. Transform the N-element frequency domain signal into a time domainsignal through inverse fast Fourier transformation (IFFT), and add acyclic prefix to the time domain signal to generate the first signal.

S303. Send the first signal in a radio frequency manner.

Optionally, during execution of S302, the time domain signal obtained bythe terminal by performing IFFT on the generated N-element frequencydomain signal is an OFDM symbol. During execution of S303, the terminalsends the first signal in a radio frequency manner. In other words, theterminal sends, on the N subcarriers, the first signal carrying thesequence {f_(n)}.

In a possible example, the terminal may send, on one OFDM symbol, thefirst signal carrying the sequence {f_(n)}, or may send, on a pluralityof OFDM symbols, the first signal carrying the sequence {f_(n)}.

Optionally, the first signal is a reference signal. Specifically, thefirst signal may be UCI and a DMRS. Alternatively, the first signal maybe acknowledgement (ACK) information, negative acknowledgement (NACK)information, or uplink scheduling request (SR) information. In thisembodiment of this application, the first signal is not limited to theforegoing information.

Optionally, the first signal is a signal used to carry communicationinformation. During specific implementation, the communicationinformation may be carried in a sequence selection manner, or may becarried in a sequence modulation manner, but is not limited thereto.

Optionally, the sequence selection manner means allocating 2^(n)orthogonal sequences to one terminal. Optionally, the 2^(n) orthogonalsequences may be 2^(n) cyclic shifts of one root sequence, and the 2^(n)orthogonal sequences can carry information of n bits. For example, the2^(n) orthogonal sequences are four sequences numbered 0, 1, 2, and 3.00 corresponds to a sequence 0, 01 corresponds to a sequence 1, 10corresponds to a sequence {2}, and 11 corresponds to a sequence 3. Inthis case, the four sequences can carry information of 2 bits.

It should be noted that in the sequence selection manner, differentvalues of a in the sequence {f_(n)} are used to indicate differentcyclic shifts. Optionally, a may carry different information.

Optionally, the sequence modulation manner means allocating one sequenceto one user and generating a modulation symbol by using information thatneeds to be transmitted by the user. The modulation symbol includes butis not limited to a BPSK symbol, a QPSK symbol, an 8QAM symbol, a 16QAMsymbol, or the like. The modulation symbol is multiplied by the sequenceto generate an actually to-be-sent sequence. For example, one BPSKsymbol may be 1 or −1, and for one sequence {f_(n)}, a to-be-sentsequence may be {f_(n)} or {−f_(n)} after modulation is performed basedon the BPSK symbol.

In a possible example, in descriptions corresponding to FIG. 2 in thespecification, after accessing the network, the terminal may determine,by using A and the sequence {x_(n)}, the sequence {f_(n)} consisting theN elements that is configured by the network device.

It should be noted that in the sequence modulation manner, differentvalues of A in the sequence {f_(n)} are used to carry differentinformation.

Optionally, A may be a modulation symbol. In this case, a datainformation bit or control information bit are modulated to obtain A. Ais carried on the N elements included in the sequence {f_(n)}, and Adoes not vary with n.

Optionally, A is a constant. For example, A=1. For example, A may be asymbol known to both the terminal and the network device. Alternatively,A may indicate an amplitude.

It should be noted that, that A is a constant in a transmission timeunit does not mean that A is fixed, and A may change when the firstsignal is sent at different moments. For example, all the N elementsincluded in the sequence {f_(n)} or the sequence {x_(n)} are a referencesignal, and A is an amplitude of the reference signal. When the terminalsends the first signal for the first time, A may be equal to 1. When theterminal sends the first signal for the second time, A may be equal to2.

S103. The network device receives the first signal carried on the Nsubcarriers, to obtain the N elements in the sequence {f_(n)}.

It can be learned from S102 that the first signal is generated byrespectively mapping the N elements in the sequence {f_(n)} consistingthe N elements to the N subcarriers. For specific descriptions of thesequence {f_(n)}, refer to the corresponding descriptions in S101 andS102, and details are not described herein again.

Optionally, during execution of S103, a process in which the networkdevice receives the first signal carried on the N subcarriers is asfollows: a time domain signal is obtained and a cyclic prefix is removedfrom the signal. Then, M-element FFT is performed on a signal obtainedafter the cyclic prefix is removed, to obtain an N-element frequencydomain signal, where M is greater than or equal to N. Then, the networkdevice receives the first signal carried on the N subcarriers. The firstsignal is the sequence {f_(n)} consisting the N elements. For example,the network device receives the signal on the N subcarriers based onlocations that are of the N subcarriers in subcarriers in thecommunications system and that are predefined or configured by thenetwork device.

During specific implementation, after the terminal accesses the network,the terminal sends a PUCCH by using the configured sequence {f_(n)}, andthe network device receives the PUCCH by using the sequence {f_(n)}configured for the terminal.

S104. The network device processes the first signal based on the Nelements in the sequence {f_(n)}.

Optionally, FIG. 5 is a schematic diagram of a process of processing thefirst signal by the network device. Through traversing a sequence{f_(n)′} that are locally stored, the network device obtains allpossible sequences. The network device separately performs correlationprocessing and maximum likelihood comparison on the obtained sequence{f_(n)} and all the possible sequences of the sequence {f_(n)′}, toobtain data transmitted by the terminal.

With reference to descriptions corresponding to S102 in thespecification, a value combination of information of 2 bits is {(0, 0),(0, 1), (1, 0), (1, 1)}. With reference to FIG. 2, when the informationof 2 bits is (0, 0), the obtained sequence {f_(n)′} is a sequence{f_(1,n)′}; when the information of 2 bits is (0, 1), the obtainedsequence {f_(n)′} is a sequence {f_(2,n)}; when the information of 2bits is (1, 0), the obtained sequence {f_(n)′} is a sequence {f_(4,n)};or when the information of 2 bits is (1, 1), the obtained sequence{f_(n)′} is a sequence {f_(4,n)′}. Correlation is separately performedbetween the sequence {f_(n)} and {f_(1,n)′}, {f_(2,n)′}, {f_(3,n)′}, and{f_(4,n)′}, to obtain four correlation values. A value of theinformation of 2 bits that is corresponding to a largest correlationvalue is data obtained by the network device. For example, if thelargest correlation value is obtained through correlation between thesequence {f_(n)} and {f_(1,n)′}, the information of 2 bits is (0, 0).

According to the sequence-based signal processing method disclosed inthis embodiment of this application, a sequence meeting a requirementfor sending a signal by using a PUCCH is determined, where the sequenceis the sequence {f_(n)} consisting the N elements, f_(n) is an elementin the sequence {f_(n)}, the determined sequence {f_(n)} is a sequencemeeting the preset condition, the preset condition isf_(n)=A·x_(n)·e^(2π·j·a·n), the value of n ranges from 0 to N−1, A is anon-zero complex number, a is a real number, j=√{square root over (−1)},the element x_(n)=u·e^(π·j·s) ^(n) ^(/4), u is a non-zero complexnumber, and the sequence {s_(n)} consisting of the elements s_(n) is asequence in the first sequence set or an equivalent sequence of asequence in the first sequence set, or a sequence in the second sequenceset or an equivalent sequence of a sequence in the second sequence set,or a sequence in the third sequence set or an equivalent sequence of asequence in the third sequence set; then, the N elements in the sequence{f_(n)} are respectively mapped to the N subcarriers to generate thefirst signal; and the first signal is sent. By using the determinedsequence, when a signal is sent from a PUCCH, a low sequence correlationcan be maintained, and a relatively small PAPR value and CM value canalso be maintained, thereby meeting a requirement of a communicationapplication environment in which a signal is sent by using a PUCCH.

Still further, based on the sequence-based signal processing methoddisclosed in this embodiment of this application, the sequence {s_(n)}that consists of the elements s_(n) and to which the sequence {f_(n)}consisting the N elements that is determined in S101 relates may be asequence in a fourth sequence set or an equivalent sequence of asequence in the fourth sequence set. A peak to average power ratio of asequence {f_(n)} corresponding to the sequence in the fourth sequenceset is less than 2.8 dB, and a value of a correlation between any cyclicshift of any one of sequences {f_(n)} corresponding to the fourthsequence set and any cyclic shift of another sequence in the sequences{f_(n)} is less than 0.52. PAPRs of many of 30 length-24 sequences inLTE are greater than 3 dB, and values of correlations between thesequences in LTE are generally relatively large through comparisonbetween correlation value distribution of the sequences in LTE andcorrelation value distribution of sequences in the fourth sequence set.

During specific implementation, the sequence in the fourth sequence setincludes at least one of the following: a sequence in a sequence set 4A,a sequence in a sequence set 4B, and a sequence in a sequence set 4C.

The sequence in the sequence set 4A includes some or all of thefollowing 30 length-18 sequences, PAPRs of the sequences are less than3.0 dB, and values of correlations between the sequences are less than0.543:

{−3, −3, 1, 1, −3, −3, −3, −3, 1, 1, −3, 1, 1, −3, 1, −3, 1, −3}, {−3,1, −3, 1, −3, 1, 1, −3, 1, 1, −3, −3, −3, −3, 1, 1, −3, −3}, {−3, 1, 1,−3, −3, 1, 1, −3, 1, −3, 1, 1, 1, 1, −3, −3, −3, −3}, {−3, 1, −3, −1, 3,−1, −1, 1, 3, −1, −1, 1, 1, 1, −1, −3, −3, −3}, {−3, 1, −3, 3, −1, 3, 3,1, −1, 3, 3, 1, 1, 1, 3, −3, −3, −3}, {−1, 1, −1, 1, 3, 1, 3, −1, −3, 3,1, 1, −3, −1, −1, 3, −3, −3}, {3, 1, 3, 1, −1, 1, −1, 3, −3, −1, 1, 1,−3, 3, 3, −1, −3, −3}, {−1, 1, −3, −1, 3, −1, −3, −1, −3, 3, 3, 1, −1,3, 3, −3, −3, −3}, {3, 1, −3, 3, −1, 3, −3, 3, −3, −1, −1, 1, 3, −1, −1,−3, −3, −3}, {3, 3, −3, −1, −3, −3, −3, 1, 1, −1, 3, −1, −1, −1, −3, 1,−3, −3}, {1, 3, −1, 1, 3, −1, −3, −3, −3, −3, 3, −1, −3, −1, 3, 1, −3,−3}, {1, −1, 3, 1, −1, 3, −3, −3, −3, −3, −1, 3, −3, 3, −1, 1, −3, −3},{1, 3, −1, −1, 3, 3, −1, 3, −1, 1, −1, −3, 3, −3, 3, −3, −3, −3}, {1,−1, 3, 3, −1, −1, 3, −1, 3, 1, 3, −3, −1, −3, −1, −3, −3, −3}, {−3, 3,−1, −1, −1, 1, 1, 3, −1, 3, −1, 1, 3, −1, −1, −1, −3, −3}, {−3, −1, 3,3, 3, 1, 1, −1, 3, −1, 3, 1, −1, 3, 3, 3, −3, −3}, {3, −1, −3, −1, 3, 3,−1, −3, −1, 1, 3, 1, 1, −3, −3, −1, −3, −3}, {−3, 1, 1, −1, 1, 3, 1, 1,−3, 3, −1, 3, −1, −1, −1, 3, −3, −3}, {3, 3, 3, −3, −3, 1, 3, −1, 3, −3,−1, 3, 1, −3, 1, −1, −3, −3}, {3, −1, −1, −3, 1, 1, −3, −3, −1, 3, 1,−3, 1, −3, −3, −3, −3, −3}, {−3, −3, −1, −3, −3, 3, −3, 3, −1, −1, 1,−1, 3, −3, 1, 1, −3, −3}, {1, 1, −1, 3, 1, 3, 3, −1, −3, 1, 3, −1, −1,1, −3, −1, −3, −3}, {−3, 1, −1, −3, −1, −3, 3, 1, 1, −3, 3, −3, −1, −3,−1, 3, −3, −3}, {−3, −1, −1, 3, −1, −3, 3, −3, 1, −1, 1, 3, 1, 3, 1, 1,−3, −3}, {3, −1, 1, −3, 1, 1, 3, −3, −3, −3, 1, −1, −3, −1, −1, −3, −3,−3}, {−1, −3, 3, 1, −1, −1, 1, −3, −1, 1, −1, 1, −1, 1, −1, 3, −3, −3},{1, −3, −1, −1, 1, 3, −1, −3, 1, −1, 1, 3, 1, 1, −3, −1, −3, −3}, {−1,−3, −1, 3, 3, −3, 1, −1, −3, 1, 1, −3, 3, −3, −1, −3, −3, −3}, {3, −1,1, 3, 1, 3, −1, −3, 1, −1, −3, −3, 3, 3, 3, 1, −3, −3}, and {1, 1, −1,−1, 1, −3, 3, −1, 3, −3, 3, −3, −1, 3, 3, 1, −3, −3}.

The sequence set 4B includes the following 31 length-18 sequences, peakto average power ratios of sequences {f_(n)} corresponding to thesequences in the sequence set are all less than 2.8 dB, and a value of acorrelation between any cyclic shift of a sequence {f_(n)} correspondingto any sequence in the sequence set and any cyclic shift of a sequence{f_(n)} corresponding to another sequence in the sequence set is lessthan 0.54:

{−3, −3, 1, 1, −3, −3, −3, −3, 1, 1, −3, 1, 1, −3, 1, −3, 1, −3}, {−3,1, −3, 1, −3, 1, 1, −3, 1, 1, −3, −3, −3, −3, 1, 1, −3, −3}, {−3, 1, 1,−3, −3, 1, 1, −3, 1, −3, 1, 1, 1, 1, −3, −3, −3, −3}, {−3, 1, −3, −1, 3,−1, −1, 1, 3, −1, −1, 1, 1, 1, −1, −3, −3, −3}, {−3, 1, −3, 3, −1, 3, 3,1, −1, 3, 3, 1, 1, 1, 3, −3, −3, −3}, {−1, 1, −1, 1, 3, 1, 3, −1, −3, 3,1, 1, −3, −1, −1, 3, −3, −3}, {3, 1, 3, 1, −1, 1, −1, 3, −3, −1, 1, 1,−3, 3, 3, −1, −3, −3}, {3, 3, −3, −1, −3, −3, −3, 1, 1, −1, 3, −1, −1,−1, −3, 1, −3, −3}, {1, 3, −1, 1, 3, −1, −3, −3, −3, −3, 3, −1, −3, −1,3, 1, −3, −3}, {1, −1, 3, 1, −1, 3, −3, −3, −3, −3, −1, 3, −3, 3, −1, 1,−3, −3}, {1, 3, −1, −1, 3, 3, −1, 3, −1, 1, −1, −3, 3, −3, 3, −3, −3,−3}, {3, 1, −1, −1, 3, 3, −1, 3, −1, −1, 1, 3, −3, 3, −3, 3, −3, −3},{−3, 3, −1, −1, −1, 1, 1, 3, −1, 3, −1, 1, 3, −1, −1, −1, −3, −3}, {−3,−1, 3, 3, 3, 1, 1, −1, 3, −1, 3, 1, −1, 3, 3, 3, −3, −3}, {3, −1, −3,−1, 3, 3, −1, −3, −1, 1, 3, 1, 1, −3, −3, −1, −3, −3}, {−3, 1, 1, −1, 1,3, 1, 1, −3, 3, −1, 3, −1, −1, −1, 3, −3, −3}, {3, 3, 3, −3, −3, 1, 3,−1, 3, −3, −1, 3, 1, −3, 1, −1, −3, −3}, {3, −1, −1, −3, 1, 1, −3, −3,−1, 3, 1, −3, 1, −3, −3, −3, −3, −3}, {3, 3, −3, 1, −1, 1, −3, 1, −1, 3,3, −1, 1, −3, −3, 3, −3, −3}, {−3, 1, −1, −3, −1, −3, 3, 1, 1, −3, 3,−3, −1, −3, −1, 3, −3, −3}, {−3, −1, −1, 3, −1, −3, 3, −3, 1, −1, 1, 3,1, 3, 1, 1, −3, −3}, {3, 1, 3, −1, 3, 1, 3, −3, 1, 1, −3, 1, 1, 1, 1,−3, −3, −3}, {−1, −3, 3, 1, −1, −1, 1, −3, −1, 1, −1, 1, −1, 1, −1, 3,−3, −3}, {3, −3, −1, −1, 3, −1, 1, −1, −3, 3, −1, −3, 1, −1, −1, −3, −3,−3}, {1, 1, −3, 3, −1, 1, −1, 1, −3, 1, 3, 3, 1, 3, 1, 1, −3, −3}, {3,−3, −1, 3, −3, 3, 3, −3, −3, −1, 3, 1, −3, 1, 1, −1, −3, −3}, {3, −3,−1, −3, 3, 1, 1, −3, 1, −3, 3, 3, −3, 1, −3, 3, −3, −3}, {1, 3, 3, −1,−1, −3, 3, 1, 3, 3, 1, 3, −3, 1, −3, 1, −3, −3}, {−1, 3, −1, 3, 1, −3,1, 1, −3, −3, −3, −1, 1, −3, −3, −3, −3, −3}, {−3, −3, −1, 3, −1, 1, 3,1, −1, −1, −3, −3, −1, −3, 1, −1, −3, −3}, and {−1, −1, 1, 1, −3, 1, −3,1, 1, −3, −3, 1, 1, −1, −3, −1, −3, −3}.

The sequence in the sequence set 4C includes some or all of thefollowing sequences, peak to average power ratios of sequencescorresponding to sequences in the sequence set are all less than 2.8 dB,and a value of a correlation between any cyclic shift of a sequencecorresponding to any sequence in the sequence set and any cyclic shiftof a sequence corresponding to another sequence in the sequence set isless than 0.56:

{3, −1, 1, −3, −3, 1, 3, 1, −3, −3, 1, −1, 3, −3, −3, −3, −3, −3}, {−1,−1, 3, 1, 3, 3, −1, 3, −3, −1, 3, −1, −3, −1, 1, −1, −3, −3}, {−1, −3,−3, −3, 1, −3, −1, 1, −3, 1, −3, 3, −1, −1, 3, 3, −3, −3}, {−3, 1, 3,−3, 3, −1, 1, 3, 1, −1, 3, −3, 3, 1, −3, −3, −3, −3}, {3, 3, 1, 1, 1,−1, 3, −1, 1, −3, 1, 1, −3, 3, 1, 3, −3, −3}, {3, 1, −3, 3, −1, 3, −3,3, −3, −1, −1, 1, 3, −1, −1, −3, −3, −3}, {−1, 1, 1, −3, 3, −1, −3, −1,3, −3, 3, −3, 3, 3, −1, −1, −3, −3}, {1, 3, −1, 3, −1, 1, −1, −1, −1, 3,3, 3, 1, −3, 3, 1, −3, −3}, {−1, 3, 1, −3, −3, −1, 3, −3, 3, 1, −1, −1,3, −3, 3, −3, −3, −3}, {−3, 1, 1, −3, 3, 3, −3, −1, −3, −1, 3, 1, −3,−1, −1, −3, −3, −3}, {−1, 3, 1, 3, −3, −1, −3, 1, −1, −3, −3, 1, 1, −3,−1, −3, −3, −3}, {1, 3, −3, −1, 3, −1, 3, −1, −3, −1, −1, 3, 1, −1, −3,−3, −3, −3}, {−3, 1, 1, −1, 1, 3, 1, 1, −3, 3, −1, 3, −1, −1, −1, 3, −3,−3}, {1, 1, 3, 3, 3, −3, 1, −1, 3, −3, 1, 1, −3, 1, −1, −1, −3, −3},{−1, 3, 1, −3, −3, 1, −1, 1, −3, −3, 1, 3, −1, −3, −3, −3, −3, −3}, {−1,3, 1, 3, −1, −3, 1, 1, 3, 1, 1, 3, 1, 1, −3, −1, −3, −3}, {−1, 1, −3, 1,−3, −3, −3, 1, −3, −3, 1, −3, 3, 1, 1, 1, −3, −3}, {1, −3, 1, −3, −1, 3,1, 3, 3, −3, 3, 1, 3, 3, 1, 1, −3, −3}, {3, 1, 3, 1, −1, 1, −1, 3, −3,−1, 1, 1, −3, 3, 3, −1, −3, −3}, {−1, −3, 1, −1, 3, −1, 1, 1, 1, −1, 1,−3, −1, 3, 1, 1, −3, −3}, {3, −3, −3, 1, −1, −3, 1, −1, −1, −1, −3, −1,3, −1, 1, −3, −3, −3}, {3, −3, 3, 1, −1, 1, 3, 1, −1, −3, 1, 3, 3, 3,−1, 3, −3, −3}, {1, −3, 3, 1, −1, 1, −1, −1, 1, 3, 1, −1, 1, −3, 1, 3,−3, −3}, {−1, 1, 1, 3, −3, 3, −1, 3, 1, −1, −3, −1, 3, −3, −1, −3, −3,−3}, {1, −3, −3, 1, 1, −3, −1, 3, −1, 3, −1, −1, 1, −1, −3, −3, −3, −3},{−1, −1, −1, −3, −3, 1, −1, 3, −3, 3, −3, 1, 1, −3, 1, 3, −3, −3}, {3,−3, 1, −1, −1, 3, 1, −3, −3, −1, 3, 3, −3, 1, −3, −3, −3, −3}, {−3, −1,1, −3, −1, −3, −3, −3, −1, −3, 1, −1, −3, 1, 1, 1, −3, −3}, {1, −3, 3,1, −3, 3, −3, 1, −3, −1, −3, −3, −1, 1, 3, −3, −3, −3}, {−3, 1, −3, −3,−3, 1, −1, −1, −1, 1, 1, −3, 1, −1, −1, 1, −3, −3}, {−1, −1, 1, −1, 3,1, −3, 1, −1, 1, −3, −1, −3, 3, 3, −1, −3, −3}, and {−3, 3, 1, −3, 3,−3, −3, −3, 3, −3, 1, 3, −3, 1, 1, 1, −3, −3}.

Still further, based on the sequence-based signal processing methoddisclosed in this embodiment of this application, a set including thesequence {s_(n)} that consists of the elements s_(n) and to which thesequence {f_(n)} consisting the N elements that is determined in S101relates may include some or all of sequences in a fifth sequence set orsome or all of equivalent sequences of sequences in the fifth sequenceset.

The sequence in the fifth sequence set includes at least one of thefollowing: a sequence in a sequence set 5A, a sequence in a sequence set5B, a sequence in a sequence set 5C, a sequence in a sequence set 5D,and a sequence in a sequence set 5E. A correlation between sequences{f_(n)} determined by using sequences in the sequence set 5D is lessthan 0.49, and a correlation between sequences {f_(n)} determined byusing sequences in the sequence set 5E is less than 0.48.

The sequence in the sequence set 5A includes some or all of thefollowing 30 length-24 sequences, peak to average power ratios ofsequences {f_(n)} corresponding to sequences in the sequence set are allless than 2.8 dB, and a value of a correlation between the sequences{f_(n)} is less than 0.53:

{−1, −1, −3, −3, 3, −3, 1, 3, −3, 1, 1, −3, 3, 1, 1, −3, 3, −1, 3, 1, 3,3, −3, −3}, {−3, 3, 1, 3, −1, 1, −3, 1, −3, 1, −1, −3, −1, −3, −3, −3,−3, −1, −1, −1, 1, 1, −3, −3}, {3, −1, −3, 1, −1, −3, 1, 3, 1, 3, −3,−3, −3, −3, 1, 3, −1, −1, −1, −3, −1, −1, −3, −3}, {−1, 1, 3, −3, −1,−1, −3, 1, −3, 1, −1, 3, 1, 3, −1, −3, −3, 3, −3, 3, 3, −1, −3, −3},{−1, 3, −1, 1, −3, 1, −1, −1, −3, 3, −3, −3, 1, 3, 3, −1, −1, 3, 3, 3,3, −3, −3, −3}, {−3, 3, −1, 1, −1, −3, −3, −3, 3, −3, −3, −3, 1, −1, −1,3, −1, −1, 3, −1, 1, 3, −3, −3}, {−1, 3, 1, −3, −1, 3, 1, −3, −1, −1,−3, 1, −1, 1, 3, −3, 3, −3, −1, 1, −1, −1, −3, −3}, {1, 1, −3, −3, −3,3, −1, −1, 3, 1, 1, −3, 1, −3, −1, 3, −3, −3, −1, −3, −1, −3, −3, −3},{−1, 1, 3, −1, 3, −3, −1, 3, 3, −3, −3, −3, 3, −3, 3, −1, 1, −1, −3, 3,1, −3, −3, −3}, {−1, 3, 3, 1, 1, −1, −1, 1, −3, 1, −3, −1, 3, 1, −3, −3,1, 1, 3, 3, −3, 3, −3, −3}, {−1, −1, −3, −3, −1, −3, 3, −3, 3, −1, −1,−3, −3, 1, 1, −3, 1, −1, 1, 3, 1, 3, −3, −3}, {3, 1, 3, 1, 3, 3, 1, −3,1, −3, 3, 3, 3, −3, −1, −1, 3, 1, 1, −3, 1, 1, −3, −3}, {1, −1, −3, 1,−3, 1, −3, −3, 1, −1, 3, −3, 1, 3, 3, −3, 3, 3, 1, 1, 3, −3, −3, −3},{3, −3, −3, −1, 1, −1, 3, −1, 1, 1, −3, 1, 1, −3, 1, 1, −1, 3, 1, 1, −1,−1, −3, −3}, {−3, −3, −1, 1, 1, −3, 3, −3, −3, 1, 3, −1, −1, 3, 3, 1,−3, 1, −3, −1, −3, −1, −3, −3}, {3, −1, −3, 1, 1, −3, −3, 1, 3, −1, 3,−1, 3, −3, −3, 1, −1, −1, −1, −3, −3, −3, −3, −3}, {−1, 3, 1, −1, −3, 3,−3, −1, 3, −1, 1, −3, −3, −3, 3, −1, 1, −1, −3, −1, −1, 1, −3, −3}, {−1,−1, 1, 1, 1, −1, −1, 3, −3, 1, −1, −1, 3, −1, 3, 1, 3, −1, 1, −1, −3, 1,−3, −3}, {−3, 1, −1, 1, 3, −3, −1, 3, 1, 3, −3, 1, −1, −3, −1, 3, 3, −1,−3, −3, −3, −1, −3, −3}, {1, −3, 3, −1, −3, 1, −3, −3, −3, −1, −1, 3,−3, 1, −3, −1, 3, 1, 1, −1, −3, −3, −3, −3}, {−1, 1, 3, −1, −1, 3, −3,−1, −3, −1, 3, −1, 3, 1, −3, 3, −3, 3, 1, −1, −3, −3, −3, −3}, {1, 1, 1,1, −3, −3, −1, −3, 3, −1, 3, −3, 3, 1, −3, −1, 3, −3, 3, −3, 1, 3, −3,−3}, {−3, −1, 3, 1, 3, −1, 3, 3, −3, 1, −1, −3, −1, −3, −1, −1, 3, 1,−1, −3, −1, −1, −3, −3}, {1, −1, −3, 1, −1, −3, −3, 3, −1, 3, −3, 3, −3,−1, −1, −3, −3, −1, 1, 1, −1, 3, −3, −3}, {1, −3, −1, 1, −1, −3, 1, −1,−3, 1, −3, −1, −1, 3, 3, 3, −3, 3, 3, 1, 1, −3, −3, −3}, {−1, 3, −1, 3,−1, 1, 1, 1, −3, −3, 3, 3, −1, −3, 1, 1, −3, −1, 1, −1, −1, 1, −3, −3},{3, 1, −3, −3, 1, −1, −1, −1, −3, −1, 1, −3, 1, −3, 1, −3, −3, −1, 1, 1,−3, −1, −3, −3}, {−3, −1, 1, 1, −3, −3, −1, 3, 1, 3, 1, −3, −1, −3, −1,−1, 1, −1, −1, 3, −1, −1, −3, −3}, {−1, 3, 1, −1, −3, −1, 3, 1, 3, −3,−1, −3, 1, −3, −1, 3, 3, −3, 1, −3, −3, −3, −3, −3}, and {−1, 3, 1, 3,1, −1, −3, −1, −3, −3, 1, 3, −3, 1, 3, −3, −3, −1, −3, −3, 3, −1, −3,−3}.

The sequence in the sequence set 5B includes some or all of thefollowing 30 length-24 sequences, peak to average power ratios ofsequences {f_(n)} corresponding to sequences in the sequence set are allless than 2.8 dB, and a value of a correlation between the sequences{f_(n)} is less than 0.5:

{−1, −3, 3, 1, 1, −3, 1, −3, −3, 1, −3, −1, −1, 3, −3, 3, 3, 3, −3, 1,3, 3, −3, −3}, {1, 3, −3, −1, 3, −1, −3, 1, −3, −1, 1, 1, 3, 3, −1, −3,3, 1, −1, −1, −3, −3, −3, −3}, {1, −1, −1, −1, 3, 3, 3, −3, −3, 1, −3,1, −3, −3, 1, −3, −3, 1, −3, −3, −3, 1, −3, −3}, {3, −3, 3, 3, 3, 3, 3,−3, −1, 1, −3, −3, 3, 1, 3, −1, −3, 1, −1, 3, 1, 1, −3, −3}, {−1, −3, 3,−1, 3, 1, 3, −1, 1, −3, −1, −3, −1, 1, 3, −3, −1, −3, 3, 3, 3, −3, −3,−3}, {−3, 3, 1, 3, −1, 1, −3, 1, −3, 1, −1, −3, −1, −3, −3, −3, −3, −1,−1, −1, 1, 1, −3, −3}, {3, −1, 3, −1, 1, −3, 1, 1, −3, −3, 3, −3, −1,−1, −1, −1, −1, −3, −3, −1, 1, 1, −3, −3}, {1, −1, 1, −3, 3, 1, 3, −1,−3, 3, −1, −3, 3, 1, −3, −1, −1, −1, −3, −1, 3, −3, −3, −3}, {−1, 3, 1,−3, 1, −1, −3, 1, 1, −1, −3, −1, 1, −3, −1, 1, 1, 1, 3, −3, −1, −3, −3,−3}, {3, −1, 1, −1, 3, −3, 1, 1, 3, −1, −3, 3, 1, −3, 3, −1, −1, −1, −1,1, −3, −3, −3, −3}, {1, −3, 3, −1, −3, −1, 3, 3, 1, −1, 1, 1, 3, −3, −1,−3, −3, −3, −1, 3, −3, −1, −3, −3}, {−3, −1, 1, −3, −3, 1, 1, −3, 3, −1,−1, −3, 1, 3, 1, −1, −3, −1, −3, 1, −3, −3, −3, −3}, {−3, 1, −3, 1, −3,−3, 1, −3, 1, −3, −3, −3, −3, −3, 1, −3, −3, 1, 1, −3, 1, 1, −3, −3},{3, −3, −3, −1, 3, 3, −3, −1, 3, 1, 1, 1, 3, −1, 3, −3, −1, 3, −1, 3, 1,−1, −3, −3}, {1, 1, −1, −3, −1, 1, 1, −3, 1, −1, 1, −3, 3, −3, −3, 3,−1, −3, 1, 3, −3, 1, −3, −3}, {−3, 1, −1, −3, 1, −3, 1, −1, −1, 3, 1, 1,−1, 1, −1, −3, −1, 1, −1, −1, 1, 3, −3, −3}, {−1, −3, −3, 1, −1, −1, −3,1, 3, −1, −3, −1, −1, −3, 1, 1, 3, 1, −3, −1, −1, 3, −3, −3}, {3, −3, 3,−1, −3, 1, 3, 1, −1, −1, −3, −1, 3, −3, 3, −1, −1, 3, 3, −3, −3, 3, −3,−3}, {−1, 3, −3, −3, −1, 3, −1, −1, 1, 3, 1, 3, −1, −1, −3, 1, 3, 1, −1,−3, 1, −1, −3, −3}, {−3, −3, 1, −1, 1, −3, 3, 1, −3, 1, −3, −1, −3, −3,3, 1, −3, −1, 1, −3, −3, −1, −3, −3}, {−3, 1, 1, −3, −1, −3, 3, −3, −3,−1, 3, −1, 1, 3, 1, 3, 3, 3, −1, 3, 1, 1, −3, −3}, {3, −3, −1, 1, 3, −1,−1, −3, −1, 3, −1, −3, −1, −3, 3, −1, 3, 1, 1, −3, 3, −3, −3, −3}, {−1,3, −1, −1, 3, 3, −1, −1, −1, 3, −1, −3, 1, 3, 1, 1, −3, −3, −3, −1, −3,−1, −3, −3}, {3, −1, 3, 1, −1, 3, −1, 1, −1, 1, 3, 1, 3, 3, −3, −1, 3,−3, −3, 1, 1, −1, −3, −3}, {3, 1, −3, 3, −3, 1, −3, −1, 3, −1, 1, 3, 3,1, 1, 3, −3, −1, 1, 1, −1, −3, −3, −3}, {−1, 1, 3, −1, 3, −1, −3, −1, 1,−3, −3, −3, −3, 1, −1, −3, 3, 3, 1, 3, 3, −1, −3, −3}, {3, −3, −1, −3,1, 3, 1, −1, −3, 1, −1, 1, −1, −3, −3, 3, −3, 3, 3, −3, −1, 3, −3, −3},{1, 3, 1, 3, −1, 1, 1, −1, 1, −3, 3, −1, −3, 3, −1, −1, 3, −3, −3, 1, 1,−1, −3, −3}, {1, 1, 3, −3, −1, −1, −3, 3, 1, 1, 1, −1, 1, 1, −1, 1, −1,3, −1, 3, −3, 1, −3, −3}, and {−3, −3, −1, −1, −3, −1, 1, −3, 1, −3, −3,3, 3, −1, −3, 3, 3, −3, 1, −1, 1, −1, −3, −3}.

The sequence in the sequence set 5C includes some or all of thefollowing 24 sequences, peak to average power ratios of sequences{f_(n)} corresponding to sequences in the sequence set are all less than2.8 dB, and a value of a correlation between the sequences {f_(n)} isless than 0.482:

{−3, −3, −3, −3, 3, −1, 1, 1, −1, 3, −3, −1, −3, 1, −1, 3, −1, 1, −3,−3, 1, 1, −3, −3}, {−3, −3, −3, −1, −1, −1, 3, −1, 1, −3, −3, 1, −3, −1,3, 1, −3, 3, 1, −1, 1, −1, −3, −3}, {−3, −3, −3, −1, 1, 3, −3, 1, 1, −3,1, 1, −1, −3, 3, 1, 1, 1, 1, −3, 1, −3, 1, −3}, {−3, −3, −3, 1, 3, −3,1, 1, −1, −1, −3, −1, −3, 1, −3, 1, −1, −3, 3, 1, 3, 3, −3, −3}, {−3,−3, −1, −3, −3, −1, −1, 3, 1, 3, −3, 3, −1, 3, −1, 3, 3, −3, 3, 1, 1,−1, −3, −3}, {−3, −3, −1, −1, 3, −1, −3, 3, −1, −3, −1, 3, 3, −3, 1, 1,1, −1, 3, −3, 1, −3, −3, −3}, {−3, −3, −1, 3, −3, 3, −3, 3, 1, −1, −3,3, 1, −3, 1, −3, 1, 1, 3, 1, 1, 3, −3, −3}, {−3, −3, 1, −3, 3, −1, −3,−1, 3, −1, 1, −1, −1, −3, −3, 3, −3, −1, 1, 3, 3, −1, −3, −3}, {−3, −3,1, −1, 1, −3, 3, 1, −3, 1, −3, −1, −3, −3, 3, 1, −3, −1, 1, −3, −3, −1,−3, −3}, {−3, −1, −3, −1, −1, −1, −3, 1, 3, −3, 3, −3, 3, 1, −1, 1, −3,3, −3, −3, 1, 1, −3, −3}, {−3, −1, −3, 1, −3, 1, 3, −1, 1, −3, −1, −1,−1, −1, −3, 3, 3, 3, −1, −3, 3, 3, −3, −3}, {−3, −1, −3, 1, 3, 3, −1, 3,1, 3, −3, 1, 1, −3, −3, 1, −3, −3, 3, 3, 3, −1, −3, −3}, {−3, −1, −3, 3,−1, −3, −3, −1, 1, 1, −1, 1, −1, 1, −3, −1, −3, 1, 1, −1, −1, 3, −3,−3}, {−3, 1, −3, −1, −1, 3, −3, −1, −1, −3, 3, −1, −1, −3, 1, −3, 1, 1,1, 1, −3, −3, −3, −3}, {−3, 1, −3, −1, 1, 3, 1, −3, 1, −1, 3, −3, −1,−3, −3, −3, 3, 1, −1, −3, 3, −3, −3, −3}, {−3, 1, −1, 1, 3, 1, −3, 3, 3,3, −3, 3, 1, 1, −1, −3, −3, −1, 3, −1, −1, 3, −3, −3}, {−3, 3, −1, −3,3, 3, 1, 1, 3, −3, 3, −1, −3, −1, 1, −3, 3, −3, −1, 1, −3, −1, −3, −3},{−3, 3, −1, 3, −1, −3, −1, −1, −3, 1, −3, −1, 1, 3, −3, −1, −1, 3, 1, 1,−3, −3, −3, −3}, {−1, −3, 1, −1, 3, 3, −3, 3, −3, 1, 3, −3, 1, −1, 1,−3, −3, −3, 3, −3, −1, −1, −3, −3}, {−1, −1, 1, −1, −3, 3, 3, −1, 3, −3,3, 3, −1, −3, −3, −1, −3, 1, −3, −1, −1, 3, −3, −3}, {−1, 1, 3, −3, 3,−3, −3, 3, −3, 1, −3, 1, −3, 1, −1, −3, −3, −1, 3, 3, 1, −1, −3, −3},{−1, 3, −3, −3, 1, −1, 1, −3, −1, −3, 1, 3, 3, 3, −3, 3, 3, 1, 1, 3, 3,1, −3, −3}, {3, −3, 1, 1, 1, −3, 3, −1, 1, 3, 1, −1, 3, −3, 1, 1, 1, 1,−3, 3, −3, −3, −3, −3}, and {3, −1, −1, −3, 1, 3, −1, 1, 3, −3, −3, 3,−3, 3, 1, 3, −1, −3, −1, −3, 3, −3, −3, −3}.

The sequence in the sequence set 5D includes some or all of thefollowing sequences:

{−1, 3, −1, 3, −1, 3, 3, −1, −1, 3, −1, −1, −1, −1, 3, 3, 3, −1, −1, 3,3, 3, 3, 3}, {3, 3, −1, −1, −1, 3, 3, −1, −1, 3, 3, −1, 3, 3, −1, 3, −1,3, −1, 3, 3, 3, 3, 3}, {−3, −3, −3, −3, −3, 1, 1, −3, −3, −3, −3, −3, 1,−3, 1, 1, −3, 1, 1, −3, 1, −3, 1, −3}, {1, −3, −1, −3, 1, −3, 1, 1, −3,−3, −3, 1, −1, −1, 3, −1, −1, 3, 3, 3, 3, 1, 3, 3}, {1, −3, 3, 1, −3, 3,−1, 1, −3, 1, 1, 3, −3, 1, 1, 1, 3, 3, 1, 1, −1, −3, −3, −3}, {−1, 3,−3, −1, 3, −3, 1, −1, 3, −1, −1, −3, 3, −1, −1, −1, −3, −3, −1, −1, 1,3, 3, 3}, {1, 1, −3, 1, 1, 3, −1, 3, −1, 3, −1, −3, −3, 1, −3, −3, −3,−3, 1, 1, 1, 1, −3, −3}, {1, −3, −1, 3, 3, −1, 3, −3, −3, −1, −3, 1, −1,3, 3, −1, −3, 1, 3, −3, −3, −3, 3, 3}, {−1, 3, 1, −3, −3, 1, −3, 3, 3,1, 3, −1, 1, −3, −3, 1, 3, −1, −3, 3, 3, 3, −3, −3}, {−1, −3, 3, 3, 1,−3, −3, 1, −1, 1, 1, −1, 3, −3, −3, 3, −3, 3, −3, −3, −1, 3, −3, −3},{−1, −3, 3, −1, −3, 1, 1, −3, 1, 3, 1, −3, −3, −3, −3, −1, 3, 3, 3, 1,−3, −1, 3, 3}, {1, 3, −3, 1, 3, −1, −1, 3, −1, −3, −1, 3, 3, 3, 3, 1,−3, −3, −3, −1, 3, 1, −3, −3}, {3, −1, −1, 1, −1, −1, −3, 1, 1, 3, 1, 1,−1, 3, 1, 3, −1, −1, −3, 1, −1, 1, −3, −3}, {3, −1, −1, 3, 1, −3, −3,−1, −1, 3, −3, 1, −1, −3, −3, 3, 1, 3, −1, 3, −3, −3, −3, −3}, {−1, 3,3, −1, 1, −3, −3, 3, 3, −1, −3, 1, 3, −3, −3, −1, 1, −1, 3, −1, −3, −3,−3, −3}, {1, 1, −3, −1, 1, 3, −3, 3, 1, −1, 1, −1, −3, 1, −3, 1, −3, −1,3, 1, 1, 3, 3, 3}, {1, −3, −3, 1, −3, 1, 1, 1, −3, −3, 1, 1, 1, −3, 1,1, 1, 1, 1, −3, 1, −3, −3, −3}, {−1, 1, 1, 1, −3, −3, −3, 3, 3, −1, 3,−1, 3, 3, −1, 3, 3, −1, 3, 3, 3, −1, 3, 3}, {−1, −3, 1, 1, 3, −3, −3,−1, −3, 3, 1, 3, 1, 1, 3, 3, −1, 3, −3, 3, −3, 1, −3, −3}, {−1, −3, −3,−1, 3, 1, −3, 1, −1, 3, 3, 1, −1, −3, 1, 1, 1, 3, 1, 3, −1, 1, −3, −3},{3, −3, −3, 3, −1, 1, −3, 1, 3, −1, −1, 1, 3, −3, 1, 1, 1, −1, 1, −1, 3,1, −3, −3}, {1, 1, −3, 3, −3, −1, −3, −3, 3, −1, 1, 3, −1, −1, 3, −3, 3,3, 3, −1, 3, 1, 3, 3}, {−3, −1, 1, −3, 1, −3, −1, 3, 1, 3, 3, 3, 1, 3,3, 3, 1, −1, −1, −3, 3, 1, 3, 3}, {3, 3, −1, 3, −1, 1, −3, 1, 3, 3, −1,3, 1, −1, −1, −3, 1, 1, 3, −3, −3, 3, 3, 3}, {−3, 3, −3, 1, −3, 1, −1,−1, −3, −3, −1, −3, −3, 1, −3, −3, −1, −3, 3, −1, −1, 1, 3, 3}, {1, 1,1, −3, 1, 1, 3, −1, 1, 1, −1, −1, −3, 3, 1, 3, −1, 3, −1, 1, 3, 1, −3,−3}, {−3, −3, −1, 3, 3, 3, −3, 3, 1, −3, 1, 1, 3, −1, 3, 1, 3, −3, 3, 3,1, −1, −3, −3}, {−1, 1, −1, 1, 3, 1, −1, −3, −1, 1, −1, 3, −1, −3, 1, 1,3, −1, −1, 1, −3, −3, 3, 3}, {1, 3, −3, −1, −1, −3, 1, 1, −1, −3, 1, −1,3, 1, 3, −3, 1, −3, 1, −3, −3, 3, 3, 3}, {−3, −3, 1, 3, −1, −1, −1, −3,−1, 1, −1, 3, 3, −1, 1, −1, −3, −1, −1, −1, 3, 1, −3, −3}, {−1, −3, 1,−3, −1, 3, 1, 3, −3, −1, 3, 3, 1, 3, 3, −1, 1, 1, 1, 1, −3, 3, 3, 3},{3, 1, −3, 3, 1, −1, 3, −3, 3, 1, 3, 1, 3, −1, 1, 3, −1, 1, 1, 3, −3,−3, −3, −3}, {1, 3, −3, −1, −3, −3, 1, 3, 1, −3, 1, −1, −1, −3, −3, 1,−3, 3, −3, −3, 3, 3, −3, −3}, {−1, 1, −3, −3, 3, 1, −1, 3, −3, −1, −1,3, −1, 1, −1, 3, −3, −3, 3, −1, 3, 1, 3, 3}, {3, 3, −1, 1, 1, 1, −1, −3,1, 1, −1, 1, 3, −1, 1, −1, −1, 3, 1, 3, 1, 3, −3, −3}, {1, −1, 3, −3, 3,1, −3, 3, −3, −1, −3, −1, −3, −1, −1, −1, 3, −3, −1, −3, −3, −1, 3, 3},{3, −3, −1, 3, 3, 1, −1, 1, −3, −1, −3, −1, 3, 1, −3, 1, −1, −3, 3, 3,−3, −3, −3, −3}, {−3, 1, 3, 1, −3, 3, 3, 1, −1, 3, −1, 1, 3, −1, 1, 1,1, −1, −1, −1, 1, 3, 3, 3}, {1, −3, 1, −3, −3, −1, 1, −3, 1, 3, −1, −3,−1, −1, −3, −1, 3, 1, −1, −3, 3, 3, 3, 3}, and {−1, 1, −1, −3, −3, 1,−1, 3, 3, −3, 1, −1, 1, −3, −1, 3, −3, 1, 1, 3, 1, 3, 3, 3}.

The sequence in the sequence set 5E includes some or all of thefollowing sequences:

{−1, 3, −1, 3, −1, 3, 3, −1, −1, 3, −1, −1, −1, −1, 3, 3, 3, −1, −1, 3,3, 3, 3, 3}, {3, 3, −1, −1, −1, 3, 3, −1, −1, 3, 3, −1, 3, 3, −1, 3, −1,3, −1, 3, 3, 3, 3, 3}, {−3, −3, −3, −3, −3, 1, 1, −3, −3, −3, −3, −3, 1,−3, 1, 1, −3, 1, 1, −3, 1, −3, 1, −3}, {1, −3, −1, −3, 1, −3, 1, 1, −3,−3, −3, 1, −1, −1, 3, −1, −1, 3, 3, 3, 3, 1, 3, 3}, {1, −3, 3, 1, −3, 3,−1, 1, −3, 1, 1, 3, −3, 1, 1, 1, 3, 3, 1, 1, −1, −3, −3, −3}, {−1, 3,−3, −1, 3, −3, 1, −1, 3, −1, −1, −3, 3, −1, −1, −1, −3, −3, −1, −1, 1,3, 3, 3}, {1, 1, −3, 1, 1, 3, −1, 3, −1, 3, −1, −3, −3, 1, −3, −3, −3,−3, 1, 1, 1, 1, −3, −3}, {−1, 3, 1, −3, −3, 1, −3, 3, 3, 1, 3, −1, 1,−3, −3, 1, 3, −1, −3, 3, 3, 3, −3, −3}, {−1, −3, 3, −1, −3, 1, 1, −3, 1,3, 1, −3, −3, −3, −3, −1, 3, 3, 3, 1, −3, −1, 3, 3}, {1, 3, −3, 1, 3,−1, −1, 3, −1, −3, −1, 3, 3, 3, 3, 1, −3, −3, −3, −1, 3, 1, −3, −3}, {1,3, −1, −1, 1, −1, 3, 1, −1, 1, 1, −3, 1, 3, 1, 3, −1, −3, −3, −1, −1,−3, 3, 3}, {−1, 1, −3, 1, 3, 3, −3, 1, −1, −1, 3, 3, 1, −1, 1, 1, −3, 1,−1, 3, 3, −3, 3, 3}, {−1, −3, 1, 1, −1, 1, −3, −1, 1, −1, −1, 3, −1, −3,−1, −3, 1, 3, 3, 1, 1, 3, −3, −3}, {−3, 1, −1, −3, 1, 1, −1, 1, −1, 1,−3, −3, 3, 3, 1, −3, 3, −3, 3, −3, −1, 1, 3, 3}, {1, 1, 3, 1, −3, −3,−1, −3, −1, 3, −3, 1, 3, 3, −3, 1, 3, 3, 3, 1, −1, −3, 3, 3}, {−1, 1,−3, −3, 3, −1, 1, −3, 3, 1, −3, −1, 1, −3, 3, −1, 3, 1, 1, 1, 1, 1, 3,3}, {1, 1, 1, −1, 1, 3, −1, 1, −1, −3, 3, 1, −3, −3, 3, −1, 1, 1, 3, −1,−3, 1, 3, 3}, {3, 3, −3, 1, −1, 3, −3, −3, −1, 3, 1, 1, −3, 3, 1, −1,−3, −1, 3, −3, −1, −3, −3, −3}, {−1, 1, −3, 1, −3, −1, −1, −1, −3, 1,−1, −1, −1, 3, 3, −3, 1, 1, 1, −1, −3, 1, −3, −3}, {−3, −3, 1, 3, 1, −1,3, −3, 3, 3, −3, −3, 1, 3, 1, −3, −3, 1, −1, −1, 3, −1, −3, −3}, {−3,−1, −1, 3, 1, −1, 3, −3, −3, 1, 3, −1, −3, 3, −1, 1, −3, 1, −3, −1, −3,−3, −3, −3}, {3, 1, −1, 3, 3, −1, −1, −3, −3, −3, −3, −3, 3, −1, 3, −1,−3, −3, 1, 3, 1, 3, −3, −3}, {3, 1, −1, 3, −3, 1, 3, −1, 3, 3, −3, 1,−1, 3, −3, −1, −1, 1, 1, −1, −3, −3, −3, −3}, {3, −1, 3, −3, −1, −3, 3,−3, 3, 1, −3, −1, −3, −3, −3, −3, −1, −1, 3, 3, 1, −1, 3, 3}, {1, 3, −3,3, 3, −3, −1, 1, −3, 3, 3, −1, 3, 3, 1, −3, 1, −1, 3, −1, −3, −1, −3,−3}, {−1, 3, −1, 1, −1, −3, 1, −3, −3, 1, −3, −3, −1, −1, 3, −3, −1, −1,1, 1, 1, −1, −3, −3}, {3, −1, 3, −1, 3, 1, −3, −1, −1, −3, −3, 3, −3,−1, 3, −3, −3, −1, −1, −3, 1, 1, 3, 3}, {−3, 3, 1, −3, 3, −1, 1, 3, −3,−3, −1, 3, −1, −3, −3, −3, −1, −1, −1, −1, 3, −3, 3, 3}, {3, −3, 3, 1,3, −3, −1, −1, 3, −1, −1, −3, −1, 1, −3, 3, 3, −3, 1, −1, 1, −1, 3, 3},and {3, 1, −1, −1, −1, 3, 3, −1, −3, 1, −3, −1, −3, 1, −1, 1, −3, −1, 1,−3, 1, 3, 3, 3}.

Optionally, a set including the sequence {s_(n)} consisting of theelements s_(n) is some or all of sequences in a sixth sequence set orsome or all of equivalent sequences of sequences in the sixth sequenceset. Peak to average power ratios of the sequences in the sixth sequenceset are all less than 5.5 dB, and a value of a correlation between anycyclic shift of a sequences {f_(n)} corresponding to any sequence in thesixth sequence set and any cyclic shift of a sequence {f_(n)}corresponding to another sequence in the sixth sequence set is less than0.75, 0.917, or 0.9.

The sequence in the sixth sequence set includes some or all of thefollowing sequences:

{−1, 1, 1, −3, −3, 3}, {−1, −3, −3, 1, 1, 3}, {−1, −3, 1, 3, 3, 1}, {1,3, −1, −3, −3, −1}, {−1, −3, −1, 1, −1, 1}, {−1, 1, −1, 1, 3, 1}, {3, 3,−1, −1, −1, −1}, {−3, −3, −3, −3, 1, 1}, {−3, 1, 1, −3, −3, 1}, {−3, −3,−3, 1, 1, 1}, {−3, 1, −1, −3, 3, 3}, {−3, −1, −1, −1, −1, −3}, {1, −3,−3, −3, −3, 1}, {−3, −1, 1, 1, −1, −3}, and {3, 1, −1, −1, 1, 3}.

Last three sequences in the sixth sequence set are sequences in the LTEstandard specification: {1, −3, −3, −3, −3, 1}, {−3, −1, 1, 1, −1, −3},and {3, 1, −1, −1, 1, 3}. Other sequences are sequences in a sequenceset A3.

Alternatively, the sequence in the sixth sequence set includes at leastone of the following: a sequence in a sequence set 6A and a sequence ina sequence set 6B.

The sequence in the sequence set 6A includes some or all of thefollowing sequences:

{−1, −3, −3, 1, 1, 3}, {−1, 1, 1, −3, −3, 3}, {1, 1, −3, 1, −1, 1}, {3,1, 3, −3, −3, 1}, {1, 1, −1, −3, 1, −3}, {1, 1, 1, 3, −3, 1}, {−3, −1,−3, −1, 3, 3}, {1, 1, −3, −3, 3, −3}, {−1, −3, −1, −1, 3, −3}, {1, 3,−1, −1, 1, −1}, {1, 1, 3, 3, −1, 3}, {1, 1, 1, −3, 3, −1}, {3, −3, 3, 1,−1, 1}, {1, 1, 1, −3, 1, −1}, {1, 1, 1, −3, 1, 3}, {1, 1, −1, −3, −1,1}, {1, 1, 3, −3, 3, 1}, {1, 1, −3, −3, 1, −3}, {1, 3, −3, 3, −3, 3},{−3, 1, −3, 3, 3, 3}, {−1, 3, −1, 1, 1, 1}, {1, 1, −3, 1, 3, 3}, {1, 1,3, −1, 3, 3}, {1, 3, −1, −3, −3, −1}, {−1, −3, 1, 3, 3, 1}, {1, 1, 3,−1, 1, −1}, {1, 1, −3, 3, −1, 1}, {1, 1, −3, −1, 3, 1}, {1, 1, −1, 3, 1,3}, {3, −1, 1, 3, 3, 1}, {1, 1, 3, −3, 1, −1}, {−3, −1, −1, 3, 1, 1},and {3, −1, −3, −1, −1, −3}.

The sequence in the sequence set 6B includes some or all of thefollowing sequences:

{1, 1, 1, −3, 1, −1}, {1, 1, −1, −3, −1, 1}, {1, 1, −3, −1, −3, −1},{−3, −1, −3, −1, 3, 3}, {1, 1, 3, 1, −1, 1}, {1, 1, −3, 1, 1, −1}, {1,1, 1, 1, −3, 3}, {1, 1, −1, 1, 3, −3}, {1, 1, −3, 3, −1, 1}, {1, 1, −3,−1, 3, 1}, {1, 3, −3, 3, −3, 3}, {1, 1, 3, −1, −3, 1}, {1, 1, −1, 1, 3,1}, {1, 1, 1, 1, −3, −1}, {1, 1, −3, 1, 1, 3}, {1, 1, 3, 1, −1, −3}, {1,1, 3, −1, 1, −1}, {1, 1, −3, −3, 1, −3}, {1, 1, −1, 3, 1, 3}, {1, 1, 1,1, −1, 3}, {1, 1, 3, −1, 3, −3}, {1, 1, −1, 3, −3, 1}, {1, 1, −3, 3, 3,3}, {3, −3, 3, 1, −1, 1}, {1, 1, −1, −1, 1, −3}, {1, 1, 1, −1, 3, 3},{1, 1, −3, −1, −1, −1}, {1, 1, 3, 1, −3, 1}, {1, 1, −1, 1, 1, −3}, {1,3, 1, 1, −3, 3}, {−3, 1, −3, 3, 3, 3}, {−1, −3, 1, 3, 3, 1}, and {1, 3,−1, −3, −3, −1}.

To-be-sent sequences corresponding to the sequences in the sequence set6A or the sequence set 6B have relatively small PAPRs and CM values. ThePAPR and the CM value are respectively less than 2.4597 dB and 4.7 dB. Avalue of a correlation between transmission sequences corresponding tothe sequences in the sequence set 6A and a value of a correlationbetween transmission sequences corresponding to the sequences in thesequence set 6B are respectively less than 0.917 and 0.9.

Generally, a sequence with a relatively small PAPR also has a relativelysmall CM value. Through verification, the foregoing sequences all havequite small CM values.

Based on the sequence-based signal processing method disclosed in thisembodiment of this application, an equivalent sequence of each sequenceset described above may be represented by {q_(n)}. An element q_(n) inthe equivalent sequence {q_(n)} meets q_(n)=s_(n)+u_(n)(mod 8).

During specific implementation, optionally, the sequence {f_(n)}including u_(n) includes:u _(n) =f+g·n(mod 8), where n=0,1, . . . , or N−1, N is a sequencelength, f∈{0,2,4,6}, and g∈{0,2,4,6}, where

(mod 8) indicates that the foregoing equation holds true afterperforming a modulo operation on both left-hand side and right-hand sideusing 8.

According to the sequence-based signal processing method provided inthis embodiment of this application, a sequence meeting a requirementfor sending a signal by using a PUCCH is determined, where the sequenceis the sequence {f_(n)} consisting the N elements, f_(n) is an elementin the sequence {f_(n)}, and the determined sequence {f_(n)} is asequence meeting the preset condition; then, the N elements in thesequence {f_(n)} are respectively mapped to the N subcarriers togenerate the first signal; and the first signal is sent. By using thedetermined sequence, when a signal is sent by using a PUCCH, a lowsequence correlation can be maintained, and a relatively small PAPRvalue and CM value can also be maintained, thereby meeting a requirementof a communication application environment in which a signal is sent byusing a PUCCH.

Based on the sequence-based signal processing method disclosed in theembodiments of this application, the embodiments of this applicationfurther disclose a signal processing apparatus and a communicationssystem for performing the sequence-based signal processing method.

As shown in FIG. 6, FIG. 6 is a schematic structural diagram of asequence-based signal processing apparatus 600 according to anembodiment of this application. The signal processing apparatus 600 maybe a communications device, or may be a chip in a communications device.The signal processing apparatus 600 includes a processing unit 601 and atransceiver unit 602.

The processing unit 601 is configured to determine a sequence {f_(n)}consisting of N elements, where f_(n) is an element in the sequence{f_(n)}, and the sequence {f_(n)} is a sequence meeting a presetcondition.

For the preset condition to which the processing unit 601 relates, referto the preset condition disclosed in the sequence-based signalprocessing method disclosed in the embodiments of this application. Thetwo preset conditions are consistent, and details are not describedherein again.

The processing unit 601 is further configured to respectively map the Nelements in the sequence {f_(n)} to N subcarriers to generate a firstsignal.

The transceiver unit 602 is configured to send the first signal.

For a corresponding operation in the signal processing apparatus 600disclosed in this embodiment of this application, refer to acorresponding operation performed in the sequence-based signalprocessing method disclosed in the embodiments of this application, anddetails are not described herein again.

With reference to the sequence-based signal processing method disclosedin the embodiments of this application, the signal processing apparatusdisclosed in this embodiment of this application may also be implementeddirectly by using a memory executed by hardware, or a memory executed bya processor, or a combination thereof.

As shown in FIG. 7, a signal processing apparatus 700 includes aprocessor 701 and a transceiver 703. Optionally, the signal processingapparatus 700 further includes a memory 702.

The processor 701 is coupled to the memory 702 by using a bus, and theprocessor 701 is coupled to the transceiver 703 by using the bus.

The processor 701 may be specifically a central processing unit (CPU), anetwork processor (NP), an application-specific integrated circuit(ASIC), or a programmable logic device (PLD). The PLD may be a complexprogrammable logical device (CPLD), a field-programmable gate array(FPGA), or generic array logic (GAL).

The memory 702 may be specifically a content-addressable memory (CAM) ora random-access memory (RAM). The CAM may be a ternarycontent-addressable memory (TCAM).

When the signal processing apparatus 700 is a communications device, thetransceiver 703 may be a radio frequency circuit. When the signalprocessing apparatus 700 is a chip in a terminal, the transceiver 703may be an input/output interface, a pin, a circuit, or the like in thechip.

The memory 702 may also be integrated into the processor 701. If thememory 702 and the processor 701 are mutually independent components,the memory 702 is connected to the processor 701. For example, thememory 702 and the processor 701 may communicate with each other byusing the bus. The transceiver 703 and the processor 701 may communicatewith each other by using the bus, or the transceiver 703 may be directlyconnected to the processor 701.

The memory 702 is configured to store an operation program, code, or aninstruction for sequence-based signal processing. Optionally, the memory702 includes an operating system and an application program, and isconfigured to store an operation program, code, or an instruction forsequence-based signal processing.

When the processor 701 or a hardware device needs to perform anoperation related to sequence-based signal processing, the processor 701or the hardware device may invoke and execute the operating program, thecode, or the instruction stored in the memory 702, to complete asequence-based signal processing process performed by the terminal inFIG. 1 to FIG. 5. For a specific process, refer to a corresponding partin the foregoing embodiment of this application, and details are notdescribed herein again.

It may be understood that, FIG. 7 shows merely a simplified design ofthe signal processing apparatus 700. During actual application, thesignal processing apparatus 700 may include any quantity oftransceivers, processors, memories, and the like, and all signalprocessing apparatuses 700 that can implement the embodiments of thisapplication fall within the protection scope of the embodiments of thisapplication.

As shown in FIG. 8, FIG. 8 is a schematic structural diagram of asequence-based signal processing apparatus 800 according to anembodiment of this application. The signal processing apparatus 800 maybe a communications device, or may be a chip in a communications device.The signal processing apparatus 800 includes a transceiver unit 801 anda processing unit 802.

The transceiver unit 801 is configured to receive a first signal carriedon N subcarriers.

The processing unit 802 is configured to obtain N elements in a sequence{f_(n)}, where the first signal is generated by respectively mapping theN elements in the sequence {f_(n)} consisting the N elements to the Nsubcarriers, f_(n) is an element in the sequence {f_(n)}, and thesequence {f_(n)} is a sequence meeting a preset condition.

For the preset condition to which the transceiver unit 802 relates,refer to the preset condition disclosed in the sequence-based signalprocessing method disclosed in the embodiments of this application. Thetwo preset conditions are consistent, and details are not describedherein again.

The processing unit 802 is further configured to process the firstsignal based on the N elements in the sequence {f_(n)}.

For a corresponding operation in the signal processing apparatus 800disclosed in this embodiment of this application, refer to acorresponding operation performed in the sequence-based signalprocessing method disclosed in the embodiments of this application, anddetails are not described herein again.

With reference to the sequence-based signal processing method disclosedin the embodiments of this application, the signal processing apparatusdisclosed in this embodiment of this application may also be implementeddirectly by using a memory executed by hardware, or a memory executed bya processor, or a combination thereof.

As shown in FIG. 9, a signal processing apparatus 900 includes aprocessor 901 and a transceiver 903. Optionally, the signal processingapparatus 900 further includes a memory 902.

The processor 901 is coupled to the memory 902 by using a bus, and theprocessor 901 is coupled to the transceiver 903 by using the bus.

The processor 901 may be specifically a CPU, an NP, an ASIC, or a PLD.The PLD may be a CPLD, an FPGA, or GAL.

The memory 902 may be specifically a CAM or a RAM. The CAM may be aTCAM.

When the signal processing apparatus 900 is a communications device, thetransceiver 903 may be a radio frequency circuit. When the signalprocessing apparatus 900 is a chip in a communications device, thetransceiver 903 may be an input/output interface, a pin, a circuit, orthe like in the chip.

The memory 902 may also be integrated into the processor 901. If thememory 902 and the processor 901 are mutually independent components,the memory 902 is connected to the processor 901. For example, thememory 902 and the processor 901 may communicate with each other byusing the bus. The transceiver 903 and the processor 901 may communicatewith each other by using the bus, or the transceiver 903 may be directlyconnected to the processor 901.

The memory 902 is configured to store an operation program, code, or aninstruction for sequence-based signal processing. Optionally, the memory902 includes an operating system and an application program, and isconfigured to store an operation program, code, or an instruction forsequence-based signal processing.

When the processor 901 or a hardware device needs to perform anoperation related to sequence-based signal processing, the processor 901or the hardware device may invoke and execute the operating program, thecode, or the instruction stored in the memory 902, to complete asequence-based signal processing process performed by the network devicein FIG. 1 to FIG. 5. For a specific process, refer to a correspondingpart in the foregoing embodiment of this application, and details arenot described herein again.

It may be understood that, FIG. 9 shows merely a simplified design ofthe signal processing apparatus 900. During actual application, thesignal processing apparatus 900 may include any quantity of interfaces,processors, memories, and the like, and all signal processingapparatuses 900 that can implement the embodiments of this applicationfall within the protection scope of the embodiments of this application.

FIG. 10 is a communications system 1000 according to an embodiment ofthis application. The communications system 1000 includes a firstcommunications device 1001 and a second communications device 1002. Thefirst communications device 1001 is a device on a transmitter side, andthe second communications device 1002 is a device on a receiver side.

The first communications device 1001 is configured to: determine asequence {f_(n)} consisting of N elements, respectively map the Nelements in the sequence {f_(n)} to N subcarriers to generate a firstsignal, and send the first signal to the second communications device1002.

The second communications device 1002 is configured to: receive thefirst signal on the N subcarriers that is sent by the firstcommunications device, obtain the N elements in the sequence {f_(n)},and process the first signal based on the N elements in the sequence{f_(n)}.

A quantity of first communications devices 1001 and a quantity of secondcommunications devices 1002 in the communications system disclosed inthis embodiment of this application are not limited. The firstcommunications device 1001 may be specifically the communicationsdevices disclosed in FIG. 6 and FIG. 7. Optionally, the firstcommunications device 1001 may be configured to perform correspondingoperations performed by the terminal in FIG. 1 to FIG. 5 in theembodiments of this application. The second communications device 1002may be specifically the communications devices disclosed in FIG. 8 andFIG. 9. Optionally, the second communications device 1002 may beconfigured to perform corresponding operations performed by the networkdevice in FIG. 1 to FIG. 5 in the embodiments of this application. For aspecific process and an execution principle, refer to the foregoingdescriptions, and details are not described herein again.

Persons skilled in the art should be aware that in the foregoing one ormore examples, functions described in this application may beimplemented by hardware, software, firmware, or any combination thereof.When being implemented by software, the foregoing functions may bestored in a computer-readable medium or transmitted as one or moreinstructions or code in the computer-readable medium. Thecomputer-readable medium includes a computer storage medium and acommunications medium, where the communications medium includes anymedium that enables a computer program to be transmitted from one placeto another. The storage medium may be any available medium accessible toa general-purpose or dedicated computer.

The embodiments in this specification are all described in a progressivemanner, for same or similar parts in the embodiments, refer to theseembodiments, and each embodiment focuses on a difference from otherembodiments. Especially, apparatus and system embodiments are basicallysimilar to the method embodiment, and therefore are described briefly;for related parts, refer to the descriptions in the method embodiment.

Finally, it should be noted that the foregoing embodiments are merelyintended to describe examples of the technical solutions of thisapplication instead of limiting this application. Although thisapplication and benefits of this application are described in detailwith reference to the foregoing embodiments, persons of ordinary skillin the art should understand that they may still make modifications tothe technical solutions described in the foregoing embodiments or makeequivalent replacements to some technical features thereof, withoutdeparting from the scope of the claims of this application.

What is claimed is:
 1. A sequence-based signal processing methodcomprising: determining, by a terminal, a sequence {f_(n)} consisting of24 elements, wherein f_(n) is an element in the sequence {f_(n)}, f_(n)meets f_(n)=x_(n)·e^(2π·j·a·n), 0≤n≤23, n is an integer, a is a realnumber, x_(n)=e^(π·j·s) ^(n) ^(/4), s_(n) is an element in a sequence{s_(n)} consisting of 24 elements, the sequence {s_(n)} belongs to asequence set, and the sequence set comprises following sequences: {−3,3, 1, 3, −1, 1, −3, 1, −3, 1, −1, −3, −1, −3, −3, −3, −3, −1, −1, −1, 1,1, −3, −3}, {−1, −3, 3, 1, 1, −3, 1, −3, −3, 1, −3, −1, −1, 3, −3, 3, 3,3, −3, 1, 3, 3, −3, −3}, {−1, −3, 3, −1, 3, 1, 3, −1, 1, −3, −1, −3, −1,1, 3, −3, −1, −3, 3, 3, 3, −3, −3, −3}, {3, −1, 3, −1, 1, −3, 1, 1, −3,−3, 3, −3, −1, −1, −1, −1, −1, −3, −3, −1, 1, 1, −3, −3}, {3, −1, 1, −1,3, −3, 1, 1, 3, −1, −3, 3, 1, −3, 3, −1, −1, −1, −1, 1, −3, −3, −3, −3},{1, −3, 3, −1, −3, −1, 3, 3, 1, −1, 1, 1, 3, −3, −1, −3, −3, −3, −1, 3,−3, −1, −3, −3}, {−3, −1, 1, −3, −3, 1, 1, −3, 3, −1, −1, −3, 1, 3, 1,−1, −3, −1, −3, 1, −3, −3, −3, −3}, {−3, 1, −3, 1, −3, −3, 1, −3, 1, −3,−3, −3, −3, −3, 1, −3, −3, 1, 1, −3, 1, 1, −3, −3}, and {3, −3, −3, −1,3, 3, −3, −1, 3, 1, 1, 1, 3, −1, 3, −3, −1, 3, −1, 3, 1, −1, −3, −3};mapping, by the terminal, the sequence {f_(n)} to 24 subcarriers togenerate a first signal; and sending, by the terminal, the first signal.2. The signal processing method according to claim 1, wherein mappingthe sequence {f_(n)} to the 24 subcarriers comprises: respectivelymapping the 24 elements in the sequence {f_(n)} to 24 consecutivesubcarriers.
 3. The signal processing method according to claim 1,wherein mapping the sequence {f_(n)} to the 24 subcarriers comprises:respectively mapping the 24 elements in the sequence {f_(n)} to 24equally spaced subcarriers.
 4. The signal processing method according toclaim 1, wherein the sequence set further comprises at least one offollowing sequences: {1, 1, −1, −3, −1, 1, 1, −3, 1, −1, 1, −3, 3, −3,−3, 3, −1, −3, 1, 3, −3, 1, −3, −3}, {−1, −3, −3, 1, −1, −1, −3, 1, 3,−1, −3, −1, −1, −3, 1, 1, 3, 1, −3, −1, −1, 3, −3, −3}, {3, −3, 3, −1,−3, 1, 3, 1, −1, −1, −3, −1, 3, −3, 3, −1, −1, 3, 3, −3, −3, 3, −3, −3},{−1, 3, −3, −3, −1, 3, −1, −1, 1, 3, 1, 3, −1, −1, −3, 1, 3, 1, −1, −3,1, −1, −3, −3}, {3, −3, −1, 1, 3, −1, −1, −3, −1, 3, −1, −3, −1, −3, 3,−1, 3, 1, 1, −3, 3, −3, −3, −3}, and {−1, 3, −1, −1, 3, 3, −1, −1, −1,3, −1, −3, 1, 3, 1, 1, −3, −3, −3, −1, −3, −1, −3, −3}.
 5. The signalprocessing method according to claim 1, wherein the first signal isdemodulation reference signal (DMRS) or uplink control information(UCI).
 6. A sequence-based signal processing apparatus, comprising: astorage medium including executable instructions; and a processorcoupled to the storage medium; wherein the executable instructions, whenexecuted by the processor, cause the apparatus to: determine a sequence{f_(n)} consisting of 24 elements, wherein f_(n) is an element in thesequence {f_(n)}, f_(n) meets f_(n)=A·x_(n)·e^(2π·j·a·n), 0≤n≤23, n isan integer, a is a real number, x_(n)=e^(π·j·s) ^(n) ^(/4), s_(n) is anelement in a sequence {s_(n)} consisting of 24 elements, the sequence{s_(n)} belongs to following sequences: {−3, 3, 1, 3, −1, 1, −3, 1, −3,1, −1, −3, −1, −3, −3, −3, −3, −1, −1, −1, 1, 1, −3, −3}, {−1, −3, 3, 1,1, −3, 1, −3, −3, 1, −3, −1, −1, 3, −3, 3, 3, 3, −3, 1, 3, 3, −3, −3},{−1, −3, 3, −1, 3, 1, 3, −1, 1, −3, −1, −3, −1, 1, 3, −3, −1, −3, 3, 3,3, −3, −3, −3}, {3, −1, 3, −1, 1, −3, 1, 1, −3, −3, 3, −3, −1, −1, −1,−1, −1, −3, −3, −1, 1, 1, −3, −3}, {3, −1, 1, −1, 3, −3, 1, 1, 3, −1,−3, 3, 1, −3, 3, −1, −1, −1, −1, 1, −3, −3, −3, −3}, {1, −3, 3, −1, −3,−1, 3, 3, 1, −1, 1, 1, 3, −3, −1, −3, −3, −3, −1, 3, −3, −1, −3, −3},{−3, −1, 1, −3, −3, 1, 1, −3, 3, −1, −1, −3, 1, 3, 1, −1, −3, −1, −3, 1,−3, −3, −3, −3}, {−3, 1, −3, 1, −3, −3, 1, −3, 1, −3, −3, −3, −3, −3, 1,−3, −3, 1, 1, −3, 1, 1, −3, −3}, and {3, −3, −3, −1, 3, 3, −3, −1, 3, 1,1, 1, 3, −1, 3, −3, −1, 3, −1, 3, 1, −1, −3, −3}, wherein map thesequence {f_(n)} to 24 subcarriers to generate a first signal; and sendthe first signal.
 7. The signal processing apparatus according to claim6, wherein the 24 elements in the sequence {f_(n)} are respectivelymapped to 24 consecutive subcarriers.
 8. The signal processing apparatusaccording to claim 6, wherein the 24 elements in the sequence {f_(n)}are respectively mapped to 24 equally spaced subcarriers.
 9. The signalprocessing apparatus according to claim 6, wherein the sequence setfurther comprises at least one of following sequences: {1, 1, −1, −3,−1, 1, 1, −3, 1, −1, 1, −3, 3, −3, −3, 3, −1, −3, 1, 3, −3, 1, −3, −3},{−1, −3, −3, 1, −1, −1, −3, 1, 3, −1, −3, −1, −1, −3, 1, 1, 3, 1, −3,−1, −1, 3, −3, −3}, {3, −3, 3, −1, −3, 1, 3, 1, −1, −1, −3, −1, 3, −3,3, −1, −1, 3, 3, −3, −3, 3, −3, −3}, {−1, 3, −3, −3, −1, 3, −1, −1, 1,3, 1, 3, −1, −1, −3, 1, 3, 1, −1, −3, 1, −1, −3, −3}, {3, −3, −1, 1, 3,−1, −1, −3, −1, 3, −1, −3, −1, −3, 3, −1, 3, 1, 1, −3, 3, −3, −3, −3},and {−1, 3, −1, −1, 3, 3, −1, −1, −1, 3, −1, −3, 1, 3, 1, 1, −3, −3, −3,−1, −3, −1, −3, −3}.
 10. The signal processing apparatus according toclaim 6, wherein the first signal is demodulation reference signal(DMRS) or uplink control information (UCI).
 11. A non-transitorycomputer-readable storage medium, comprising computer-executableinstructions, wherein the computer-executable instructions, whenexecuted by a computer, cause the computer to: determine a sequence{f_(n)} consisting of 24 elements, wherein f_(n) is an element in thesequence {f_(n)}, f_(n) meets f_(n)=A·x_(n)·e^(2π·j·a·n), 0≤n≤23, n isan integer, a is a real number, x_(n)=e^(π·j·s) ^(n) ^(/4), s_(n) is anelement in a sequence {s_(n)} consisting of 24 elements, the sequence{s_(n)} belongs to following sequences: {−3, 3, 1, 3, −1, 1, −3, 1, −3,1, −1, −3, −1, −3, −3, −3, −3, −1, −1, −1, 1, 1, −3, −3}, {−1, −3, 3, 1,1, −3, 1, −3, −3, 1, −3, −1, −1, 3, −3, 3, 3, 3, −3, 1, 3, 3, −3, −3},{−1, −3, 3, −1, 3, 1, 3, −1, 1, −3, −1, −3, −1, 1, 3, −3, −1, −3, 3, 3,3, −3, −3, −3}, {3, −1, 3, −1, 1, −3, 1, 1, −3, −3, 3, −3, −1, −1, −1,−1, −1, −3, −3, −1, 1, 1, −3, −3}, {3, −1, 1, −1, 3, −3, 1, 1, 3, −1,−3, 3, 1, −3, 3, −1, −1, −1, −1, 1, −3, −3, −3, −3}, {1, −3, 3, −1, −3,−1, 3, 3, 1, −1, 1, 1, 3, −3, −1, −3, −3, −3, −1, 3, −3, −1, −3, −3},{−3, −1, 1, −3, −3, 1, 1, −3, 3, −1, −1, −3, 1, 3, 1, −1, −3, −1, −3, 1,−3, −3, −3, −3}, {−3, 1, −3, 1, −3, −3, 1, −3, 1, −3, −3, −3, −3, −3, 1,−3, −3, 1, 1, −3, 1, 1, −3, −3}, and {3, −3, −3, −1, 3, 3, −3, −1, 3, 1,1, 1, 3, −1, 3, −3, −1, 3, −1, 3, 1, −1, −3, −3}, wherein map thesequence to 24 subcarriers to generate a first signal; and send thefirst signal.
 12. The non-transitory computer-readable storage mediumaccording to claim 11, wherein the 24 elements in the sequence {f_(n)}are respectively mapped to 24 consecutive subcarriers.
 13. Thenon-transitory computer-readable storage medium according to claim 11,wherein the 24 elements in the sequence {f_(n)} to 24 are respectivelymapped to equally spaced subcarriers.
 14. The non-transitorycomputer-readable storage medium according to claim 11, wherein thesequence set further comprises at least one of following sequences: {1,1, −1, −3, −1, 1, 1, −3, 1, −1, 1, −3, 3, −3, −3, 3, −1, −3, 1, 3, −3,1, −3, −3}, {−1, −3, −3, 1, −1, −1, −3, 1, 3, −1, −3, −1, −1, −3, 1, 1,3, 1, −3, −1, −1, 3, −3, −3}, {3, −3, 3, −1, −3, 1, 3, 1, −1, −1, −3,−1, 3, −3, 3, −1, −1, 3, 3, −3, −3, 3, −3, −3}, {−1, 3, −3, −3, −1, 3,−1, −1, 1, 3, 1, 3, −1, −1, −3, 1, 3, 1, −1, −3, 1, −1, −3, −3}, {3, −3,−1, 1, 3, −1, −1, −3, −1, 3, −1, −3, −1, −3, 3, −1, 3, 1, 1, −3, 3, −3,−3, −3}, and {−1, 3, −1, −1, 3, 3, −1, −1, −1, 3, −1, −3, 1, 3, 1, 1,−3, −3, −3, −1, −3, −1, −3, −3}.
 15. The non-transitorycomputer-readable storage medium according to claim 11, wherein thefirst signal is demodulation reference signal (DMRS) or uplink controlinformation (UCI).